ZAG Handbook of Modern Algebraic Geometry by Cheltsov, Ivan; Martinez-Garcia, Jesus;

Rövid leírás:

ZAG Handbook of Algebraic Geometry provides an expansive collection of extended summaries of all the research talks given at the worldwide ZAG (Zoom Algebraic Geometry) Seminar as well as contributed short notes.

Hosszú leírás:

ZAG Handbook of Algebraic Geometry provides an expansive collection of extended summaries of all the research talks given at the worldwide ZAG (Zoom Algebraic Geometry) Seminar as well as contributed short notes. Constructed from contributions from 2020-24 by active research algebraic geometers from all continents, the book is aimed at researchers in algebraic geometry and related fields who want to gain a comprehensive understanding of state-of-the-art research in algebraic geometry. The book is extensive and wide-ranging, and offers material suitable to multiple levels of readership: from advanced undergraduate students in mathematics to active specialised researchers.

Features

· A showcase of the most important worldwide trends in algebraic geometry in recent years

· Over two hundred short summaries of state-of-the-art research in algebraic geometry accessible to other mathematicians

· A combination of contributions by renowned mathematicians, key researchers and new talent

· Links to recordings of hour-long presentations for each contribution

Ivan Cheltsov is a Professor at the University of Edinburgh, United Kingdom, and his research interests include birational geometry and K-stability of Fano varieties. He is the author of 3 books and 126 articles written together with 52 co-authors. Ivan has organized research meetings in Auckland, Beijing, Cambridge, Durham, Edinburgh, Fuerteventura, Istanbul, Levico Terme, London, Magadan, Melbourne, Moscow, New York, Oberwolfach, Pipa, Pohang, Easter Island, Shanghai, Sochi, Spitsbergen, Stony Brook, Sydney, Tianjin, Wakkanai, and Vladivostok. Since 1995, Ivan has been married to Elena Cheltsova: they have three children (Ivan, Fedor, Ekaterina) and a cat, Kuzya. Aside from Mathematics, Ivan enjoys traveling, reading, and cycling his Brompton bicycle.

Jesus Martinez-Garcia is a Senior Lecturer in Pure Mathematics at the University of Essex, United Kingdom. He obtained his PhD at the University of Edinburgh in 2013 and has held research positions at the University of Bath, United Kingdom, Johns Hopkins University, United States, and the Max Planck Institute for Mathematics, Germany. His research is in algebraic geometry with special emphasis on birational geometry, moduli spaces, K-stability, Fano varieties, and computational algebraic geometry. Martinez-Garcia has written one book, several research articles, and two software packages, and he has co-organized more than ten research meetings, including the annual international conference AGGITatE, as well as several research seminars.

Tartalomjegyzék:

Table of Contents

1.          Algebraic geometry in the times of Covid
Ivan Cheltsov and Jesus Martinez-Garcia

2.          Models of Fano 3-folds
Hamid Abban

3.          Weighted Ehrhart polynomials and series for the standard simplex
Praise Adeyemo

4.          Advances in moduli theory
Jarod Alper

5.          Normal form of a holomorphic Lagrangian submanifold
Ekaterina Amerik

6.          Koszul modules and applications
Marian Aprodu

7.          Euler characteristics of aspherical Kähler manifolds
Donu Arapura

8.          Birational geometry of Calabi-Yau pairs and Cremona transformations
Carolina Araujo

9.          Enumerating punctured log maps via wall-crossing
Hulya Arguz

10.       Biregular and birational geometry of rational nodal quartic double solids
Artem Avilov

11.       Chern character of quantizable sheaves
Vladimir Baranovsky and Victor Ginzburg

12.       Vector bundles on Fano threefolds and K3 surfaces
Arnaud Beauville

13.       Cylinders in Del Pezzo surfaces with Du Val singularities
Grigory Belousov

14.       Approximation of differentiable submanifolds by real algebraic subvarieties
Olivier Benoist

15.       Kähler-Einstein metrics, Archimedean zeta functions and phase transitions
Robert Berman

16.       Geometry of 3-dimensional Del Pezzo fibrations in positive characteristic
Fabio Bernasconi

17.       Geometry of polarised varieties
Caucher Birkar

18.       On properness of K-moduli spaces and optimal destabilizations
Harold Blum

19.       Surface with ample canonical bundle and Kuranishi space a nonreduced point
Christian Boehning

20.       Projective geometry approach to the Jacobian conjecture
Alexander Borisov

21.       Explicit equations of surfaces of general type
Lev Borisov

22.       General type results for moduli of hyperkähler varieties
Emma Brakkee

23.       Geometric structures on spaces of quadratic differentials
Tom Bridgeland

24.       Extending Tom and Jerry for Fano 3-folds
Gavin Brown, Stephen Coughlan and Tom Ducat

25.       Supercycles and stable supermaps
Ugo Bruzzo and Daniel Hernandez Ruiperez

26.       Arcs and singularities
Nero Budur

27.       Chern–Weil theory and Hilbert–Samuel theorem for semipositive singular toroidal metrics
Jose Ignacio Burgos Gil

28.       Index 2 Fano 3-folds and double covers
Livia Campo

29.       Uniqueness of enhancements of triangulated categories
Alberto Canonaco, Amnon Neeman and Paolo Stellari

30.       On the birational geometry of foliations
Paolo Cascini

31.       Effective cones of moduli spaces of stable rational curves and blown up toric surfaces           Ana-Maria Castravet

32.       Nodal surfaces, coding theory, and cubic discriminants
Fabrizio Catanese

33.       The minimal model program for arithmetic surfaces enriched by a Brauer class
Daniel Chan

34.       Low dimensional components in the K-moduli of smoothable Fano 3-folds   
Ivan Cheltsov

35.       Remarks on n-folds of type (1,n)
Jungkai Chen

36.       Singularities on toric fibrations
Yifei Chen and Caucher Birkar

37.       On the distribution of canonical volumes and moduli spaces of varieties of general type
Meng Chen

38.       Subadditivity theorem for Okounkov bodies
Sung Rak Choi

39.       Enumeration of Terracini schemes
Ciro Ciliberto

40.       Numerical characterization of complex torus quotients
Benoit Claudon

41.       Slope inequalities and ample cone of KSB moduli spaces
Giulio Codogni

42.       The cohomology of the moduli space of sheaves on surfaces
Izzet Coskun

43.       Orbifold quot schemes via the le Bruyn–Procesi theorem
Alastair Craw

44.       On quadratic points on intersections of two quadrics
Brendan Creutz and Bianca Viray

45.       Deformations of exterior differential ideals and applications
Fernando Cukierman

46.       Log minimal model program for Kähler 3-folds
Omprokash Das

47.       CSCK metrics on rank one spherical Fano fourfolds
Thibaut Delcroix

48.       K-stability of P^3 blown up along the disjoint union of a twisted cubic curve and a line
Elena Denisova

49.       Stability of fibrations
Ruadhai Dervan

50.       Wall crossing for K-moduli spaces of plane curves
Kristin DeVleming

51.       The bottleneck degree of algebraic varieties
Sandra Di Rocco

52.       Dynamical filtrations|
Tien-Cuong Dinh, Hsueh-Yung Lin, Keiji Oguiso and De-Qi Zhang

53.       Roth's theorem for adelic curves
Paolo Dolce and Francesco Zucconi

54.       Enumerative geometry, fredholm analysis and moduli spaces of surfaces of general type      Simon Donaldson

55.       Bounding the complexity of 2-loop Feynman integrals
Charles Doran

56.       K-stability of P^3 blown up along smooth curves of genus 4 and degree 6
Tiago Duarte Guerreiro

57.       Rigidity of affine Brieskorn-Pham threefolds
Adrien Dubouloz

58.       Birational geometry and cylindricity of Severi-Brauer varieties
Adrien Dubouloz, Kento Fujita, Takashi Kishimoto and Takuzo Okada

59.       Okawa's theorem and wide subcategories of coherent sheaves on curves
Alexey Elagin

60.       Mixed Hodge structure decomposition of alexander modules into generalized eigenspaces
Eva Elduque

61.       Local stability threshold of Del Pezzo surfaces of degree 2
Erroxe Etxabarri Alberdi

62.       Rational simple connectedness and the quintic Del Pezzo threefold
Andrea Fanelli

63.       K3 structures from singular Fano varieties
Enrico Fatighenti

64.       An overview of homotopy path algebras
David Favero

65.       Quasi-invariants and free arrangements
Misha Feigin

66.       The Brasselet-Schurmann-Yokura conjecture on L-classes of singular varieties
Javier Fernandez de Bobadilla and Irma Pallares Torres

67.       Notes on motivic integration on Berkovich spaces
Tommaso de Fernex

68.       Counting sheaves by counting curves
Soheyla Feyzbakhsh and Richard Thomas

69.       On the boundedness of elliptically fibered Calabi-Yau threefolds
Stefano Filipazzi

70.       Connected algebraic groups acting on Fano fibrations over P^1
Enrica Floris

71.       Maximal automorphism groups of surfaces
Pascal Fong and Matilde Maccan

72.       A canonical Hodge theoretic projective structure on compact Riemann surfaces
Paola Frediani

73.       On extremal contractions of log canonical pairs
Osamu Fujino

74.       On the singular loci of higher secant varieties of Veronese embeddings
Katsuhisa Furukawa

75.       The Bourbaki degree of a plane curve
Daniel Futata and Marcos Jardim

76.       Compactifications of the moduli space of marked cubic surfaces
Patricio Gallardo

77.       Intrinsic mirrors for minimal adjoint orbits
Elizabeth Gasparim

78.       On a generalized Batyrev’s cone conjecture
Yoshinori Gongyo

79.       Complex curves in hypercomplex nilmanifolds
Iulia Gorginian

80.       Projective flatness over Klt spaces and characterisation of finite quotients of projective spaces
Daniel Greb

81.       Distinguishing triangle-free level-one phylogenetic networks using computational algebraic geometry
Elizabeth Gross

82.       Open FJRW theory and mirror symmetry: a ZAG lecture
Mark Gross, Tyler Kelly and Ran Tessler

83.       Recent progress in the MMP for 3-folds and 4-folds in char p>0
Christopher Hacon

84.       Rationality questions on Seshadri constants
Krishna Hanumanthu

85.       Log symplectic pairs and mixed Hodge structures
Andrew Harder

86.       Gaps between lc pairs and Klt pairs in a viewpoint of the minimal model theory
Kenta Hashizume

87.       Constructing new Q-Fano threefolds using Laurent inversion
Liana Heuberger

88.       Fano manifolds such that the tangent bundle is (not) big
Andreas Hoering

89.       Geometric extension
Chris Hone and Geordie Williamson

90.       An algebro-geometric higher Szemeredi lemma
Ehud Hrushovski

91.       A dynamical approach to generalized Weil's Riemann hypothesis and semisimplicity           Fei Hu

92.       Torelli problem on logarithmic sheaves
Sukmoon Huh

93.       Minimal rational curves and 1-flat cone structures
Jun-Muk Hwang

94.       A bound of the number of weighted blow-ups to compute the minimal log discrepancy for smooth 3-folds 
Shihoko Ishii

95.       The McKay correspondence
Yukari Ito

96.       Shafarevich's conjecture for canonically polarized varieties revisited
Ariyan Javanpeykar, Steven Lu, Ruiran Sun and Kang Zuo

97.       Symmetries of Fano varieties
Lena Ji

98.       Minimal log discrepancies in dimension three
Chen Jiang

99.       Equilateral convex triangulations of RP^2 with three conical points of equal defec
Nikita Kalinin

100.    1-dimensional K-moduli spaces of Fano 3-folds
Anne-Sophie Kaloghiros

101.    A brief survey on stability of tangent bundles on Fano manifolds
Akihiro Kanemitsu

102.    Are Klt Fano varieties of small volume stably rational?
Ilya Karzhemanov

103.    New examples of surgery invariant counts in real algebraic geometry
Slava Kharlamov

104.    Hodge sheaves for singular families
Sandor Kovacs

105.    Secant varieties of real curves
Mario Kummer

106.    Sextic double solids
Alexandra Kuznetsova

107.    On effective cones of rational surfaces
Antonio Laface

108.    The rational chow rings of M_7, M_8 and M_9
Hannah Larson

109.    A Néron-Ogg-Shafarevich criterion for K3 surfaces
Chris Lazda

110.    Derived categories and motives of moduli spaces of vector bundles on curves
Kyoung-Seog Lee

111.    Dominant rational maps from a very general hypersurface
Yongnam Lee

112.    Valuative stability of polarised varieties
Eveline Legendre

113.    Rational curves on Del Pezzo surfaces in positive characteristic
Brian Lehmann

114.    Codimension 2 cycles of classifying spaces of low-dimensional algebraic tori
Nicole Lemire

115.    Locally free twisted sheaves of infinite rank
Max Lieblich

116.    Rational curves on K3 surfaces
Christian Liedtke

117.    Automorphisms of projective hypersurfaces
Alvaro Liendo

118.    Motivic invariants of birational maps Hsueh-Yung Lin
Evgeny Shinder

119.    A motivic version of topological mirror symmetry
Fransois Loeser

120.    Poisson and symplectic geometry of the moduli spaces of Higgs bundles
Marina Logares

121.    On non-rationality of degenerations of Del Pezzo surfaces
Konstantin Loginov

122.    A conjecture on D algebras
Leonid Makar-Limanov

123.    Fano threefolds of Picard rank 2 and volume 28
Joseph Malbon

124.    Birational involutions of the real projective plane fixing an irrational curve
Frederic Mangolte

125.    Unirationality of instanton moduli space for small charges
Dimitri Markushevich and Alexander Tikhomirov

126.    The defect of a cubic threefold
Lisa Marquand

127.    The determinant of cohomology and moduli of lambda-connections
Johan Martens

128.    Two remarks on asymptotically log Fano pairs
Jesus Martinez-Garcia

129.    On K-stability of Calabi-Yau fibrations
Hattori Masafumi

130.    On the (uni)rationality problem for hypersurfaces
Alex Massarenti

131.    Transformations of transfinite diameter
Sione Ma`u

132.    Perverse-Hodge octahedron
Mirko Mauri

133.    A special rational surface
Massimiliano Mella

134.    On the top-weight rational cohomology of A_g
Margarida Melo

135.    Jordan property for automorphism groups
Sheng Meng

136.    Geometry and arithmetic of equivariant compactifications of the affine space
Pedro Montero

137.    Special variational Hodge conjecture for toric varieties
William Montoya

138.    Tropical geometry and phylogenetic diversity
Han-Bom Moon

139.    Fundamental groups of singularities of the MMP
Joaquin Moraga

140.    A moduli space in the differential geometry world
David Mumford

141.    Interview with David Mumford
Ivan Cheltsov and Jesus Martinez-Garcia

142.    The Kawamata–Viehweg vanishing theorem for schemes
Takumi Murayama

143.    Minimal exponent and Hodge filtrations
Mircea Mustata

144.    Inversion of adjunction for quotient singularities
Yusuke Nakamura

145.    On compatifying moduli and degenerations of K-trivial varieties
Yuji Odaka

146.    K-stability and birational superrigidity for Fano 3-fold weighted hypersurfaces
Takuzo Okada

147.    Moduli space of semiorthogonal decompositions
Shinnosuke Okawa

148.    Stable irrationality of the very general quartic fivefold
John Christian Ottem

149.    Contact in algebraic and tropical geometry
Marco Pacini and Damiano Testa

150.    Extended abstract of counting divisorial contractions with centre a cA_n-singularity
Erik Paemurru

151.    Fine compactified Jacobians of nodal curves
Nicola Pagani

152.    On polynomial automorphisms commuting with a simple derivation
Ivan Pan

153.    K-moduli for log Fano complete intersections
Theodoros Stylianos Papazachariou

154.    Cayley octads, plane quartic curves, Del Pezzo surfaces of degree 2, and double Veronese cones
Jihun Park

155.    A Castelnuovo-Mumford regularity bound for threefolds with rational singularitie
Jinhyung Park

156.    Moderately discontinuous algebraic topology and singularities
Maria Pe Pereira

157.    Generic flexibility of cubic cones
Alexander Perepechko

158.    Serre functors of semiorthogonal components
Alex Perry

159.    Deformations of toric singularities and applications to K-moduli of Fano varieties
Andrea Petracci

160.    Campana points on Fano varieties
Marta Pieropan

161.    On canonical threefolds near the noether line
Roberto Pignatelli

162.    K-stability and space sextic curves of genus three
Antoine Pinardin

163.    On local-global principles and Galois cohomology
Alena Pirutka

164.    Conic-line arrangements in the complex projective plane
Piotr Pokora

165.    Hyperelliptic limits of quadrics through canonical curves and the super-Schottky locus
Alexander Polishchuk

166.    General elephants for 3-fold extremal contractions
Yuri Prokhorov

167.    Rationally connected rational double covers of primitive Fano varieties
Aleksandr Pukhlikov

168.    Singularities and divisors in the moduli space of surfaces
Julie Rana

169.    Sheaf counting of Hilbert schemes of points on C^4
Jorgen Rennemo

170.    Wall-crossing pathologies in three dimensions
Fatemeh Rezaee

171.    K-polystability of smooth Fano SL_2-threefolds
Jack Rogers

172.    Hodge-Riemann classes and schur polynomials
Julius Ross

173.    The splendour of asymptotically log Del Pezzos
Yanir Rubinstein

174.    Smoothing toroidal crossing Fano 3-folds
Helge Ruddat

175.    An overview on mordell–Weil rank jumps for fibers of elliptic surfaces
Cecilia Salgado

176.    Blow-ups with log canonical singularities
Gregory Sankaran

177.    On birational boundedness of some Calabi–Yau hypersurfaces
Taro Sano

178.    Equivariant solidity of the three-dimensional projective space
Arman Sarikyan

179.    Near-rationality properties of norm varieties
Anand Sawant

180.    Generalized hyperpolygons and applications
Laura Schaposnik

181.    Equality in the Bogomolov-Miyaoka-Yau inequality in the non-general type case
Stefan Schreieder

182.    Rational curves on Enriques surfaces, but only few
Matthias Schuett

183.    Cohomology of the moduli of Higgs bundles and the Hausel-Thaddeus conjecture
Junliang Shen

184.    Survey of the article on Atiyah class and sheaf counting on local Calabi-Yau fourfolds
Artan Sheshmani

185.    Automorphism groups of complex elliptic surfaces
Constantin Shramov

186.    Lebrun-Salamon conjecture from the effective nonvanishing for Fano manifolds
Robert Smiech

187.    Partial order on involutive permutations and double Schubert cells
Evgeny Smirnov

188.    Geometric aspects of Kähler-Einstein metrics on Klt pairs: a remark on optimal Bogomolov-Miyaoka-Yau inequality
Cristiano Spotti

189.    Weak Del Pezzo surfaces with global vector fields
Claudia Stadlmayr

190.    Local volumes of singularities and the mahler conjecture for convex bodies
Hendrik Suess

191.    Higher order minimal families of rational curves on Fano manifolds
Taku Suzuki

192.    An O-acyclic variety of even index
Fumiaki Suzuki

193.    The Mukai model of M_7
David Swinarski

194.    Local effectivity in projective spaces
Tomasz Szemberg

195.    Fermat type arrangements and the containment problem
Justyna Szpond

196.    Birational properties of base spaces of smooth projective families of good minimal models
Behrouz Taji

197.    Key varieties for prime Q-Fano threefolds of codimension 4
Hiromichi Takagi

198.    Deformations of F-pure and F-regular singularities
Shunsuke Takagi

199.    On Mori fibre spaces in positive characteristic
Hiromu Tanaka

200.    Rational curves on Fano threefolds
Sho Tanimoto

201.    Delta invariants of quasi-smooth hypersurfaces
Luca Tasin

202.    Real structures on almost homogeneous varieties
Ronan Terpereau

203.    Mirror symmetry for fibrations and degenerations
Alan Thompson

204.    On a logarithmic version of a theorem of Enriques
Sofia Tirabassi

205.    Equivariant birational types
Yuri Tschinkel

206.    Vector fields on canonically polarized surfaces
Nikos Tziolas

207.    Noncommutative Del Pezzo surfaces
Kazushi Ueda

208.    Exceptional collections on Σ_2
Hokuto Uehara

209.    Counts of secant planes to varieties, degenerations, and universal polynomials
Mara Ungureanu

210.    Actions of Cremona groups on CAT(0) cube complexes
Christian Urech

211.    Artin-Mumford counterexample, with generalizations, via Enriques surfaces
Alessandro Verra

212.    Higher Fano manifolds
Nivedita Viswanathan

213.    Global Brill-Noether theory over the Hurwitz space
Isabel Vogt

214.    Positivity of the second exterior power of the tangent bundles
Kiwamu Watanabe

215.    Pinched handle decompositions of finite simplicial complexes
Jean-Yves Welschinger

216.    Concurrent exceptional curves on Del Pezzo surfaces of degree one and torsion points on elliptic fibrations
Rosa Winter

217.    Rational maps via C^*-actions
Jaroslaw Wisniewski

218.    On weighted Del Pezzo hypersurfaces
Joonyeong Won

219.    Equivariant birational geometry of linear actions
Kaiqi Yang

220.    Equivariant birational rigidity: around one question of Cheltsov and Kollár
Egor Yasinsky

221.    Stringy motives and local fundamental groups of Klt surface singularities in arbitrary characteristic
Takehiko Yasuda

222.    Degenerations, fibrations and mirror symmetry
Fenglong You

223.    Stability of pencils of plane curves
Aline Zanardini

224.    Jordan properties of automorphism groups of algebraic varieties and complex manifolds
Yuri Zarhin

225.    Basis divisors and balanced metrics
Kewei Zhang

226.    The moduli space of cubic surface pairs via the intermediate Jacobians of Eckardt cubic threefolds
Zheng Zhang

227.    Equivariant geometry of singular cubic threefolds
Zhijia Zhang

228.    Topological SYZ fibrations with discriminant in codimension 2
Ilia Zharkov

229.    Compact Kähler threefolds with the action of an abelian group of maximal dynamical rank
Guolei Zhong

230.    Equivariant K-stability under finite group action
Ziwen Zhu

231.    K-stability of Fano varieties via admissible flags
Ziquan Zhuang

232.    Unbounded connected algebraic subgroups of birational transformations
Sokratis Zikas

233.    Finite quotients of Cremona groups
Susanna Zimmermann