Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics by Greuel, Gert-Martin; Narváez Macarro, Luis; Xambó-Descamps, Sebastià;

Hosszú leírás:

This volume brings together recent, original research and survey articles by leading experts in several fields that include singularity theory, algebraic geometry and commutative algebra. The motivation for this collection comes from the wide-ranging research of the distinguished mathematician, Antonio Campillo, in these and related fields. Besides his influence in the mathematical community stemming from his research, Campillo has also endeavored to promote mathematics and mathematicians' networking everywhere, especially in Spain, Latin America and Europe. Because of his impressive achievements throughout his career, we dedicate this book to Campillo in honor of his 65th birthday.

Researchers and students from the world-wide, and in particular Latin American and European, communities in singularities, algebraic geometry, commutative algebra, coding theory, and other fields covered in the volume, will have interest in this book.

Tartalomjegyzék:

Preface.- Antonio Campillo: A Portrayal of his Life and Work.- Singularities in Positive Characteristic Equisingularity, Classification, Determinacy: Dedicated to Antonio Campillo on the occasion of his 65th birthday.- Ultrametric spaces of branches on arborescent singularities.- Two points of the boundary of toric geometry.- On the Milnor formula in arbitrary characteristic.- Foliations in the plane uniquely determined by minimal subschemes of its singularities.- Newton transformations and the motivic Milnor fiber of a plane curve.- Nash modification on toric curves.- A recursive formula for the motivic Milnor fiber of a plane curve.- On Hasse--Schmidt derivations: the action of substitution maps.- An introduction to resolution of singularities via the multiplicity.- Platonic Surfaces.- Coverings of rational ruled normal surfaces.- Ulrich bundles on Veronese surfaces.- Multiple structures on smooth on singular varieties.- Smoothness in a family of varieties with dihedral symmetry and the DFT matrix.- The Greedy Algorithm and the Cohen-Macaulay property of rings, graphs and toric projective curves.- Binomial ideals and congruences on $\mathbb{N}^n$.- The $K$-theory of toric schemes over regular rings of mixed characteristic.- On finite and nonfinite generation of associated graded rings of Abhyankar valuations.- Symbolic powers of monomial ideals and Cohen-Macaulay vertex-weighted digraphs.- Asymptotics of reduced algebraic curves over finite fields.- The Poincaré polynomial of a linear code.- The Metric Structure of Linear Codes.- On some properties of $A$ inherited by $C_{b}(X,A)$.- A fractional partial differential equation for theta functions.- On continued fractions.