Enriques Surfaces I
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Product details:
- Edition number Second Edition 2025
- Publisher Springer
- Date of Publication 29 May 2025
- Number of Volumes 1 pieces, Book
- ISBN 9789819612130
- Binding Hardback
- No. of pages681 pages
- Size 235x155 mm
- Language English
- Illustrations 29 Illustrations, black & white; 14 Illustrations, color 700
Categories
Short description:
This book, consisting of two volumes, gives a contemporary account of the study of the class of projective algebraic surfaces known as Enriques surfaces. These surfaces were discovered more than 125 years by F. Enriques in an attempt to extend the characterization of rational algebraic curves to the case of algebraic surfaces. The novel feature of the present exposition is that no assumption on the characteristic of the ground field is assumed.
This requirement calls for exploring the geometry of such surfaces by purely geometric and arithmetic methods that do not rely on transcendental methods such as the theory of periods of algebraic surfaces of type K3, which are close relatives of Enriques surfaces.
Some of the methods use many technical tools from algebraic geometry that are discussed in Volume 1 and may be a useful source of references for the study of algebraic surfaces over fields of positive characteristic. Volume 1 also contains a detailed exposition of the theory of elliptic surfaces over fields of arbitrary characteristic.
The first volume is an essential and greatly extended revision of Enriques Surfaces I, published in 1989 by Birkhäuser and co-authored by F. Cossec and I. Dolgachev. Included is a new chapter devoted to the theory of moduli of Enriques surfaces.
The two volumes together contain many examples and an extensive bibliography made up of more than 700 items.
MoreLong description:
This book, consisting of two volumes, gives a contemporary account of the study of the class of projective algebraic surfaces known as Enriques surfaces. These surfaces were discovered more than 125 years by F. Enriques in an attempt to extend the characterization of rational algebraic curves to the case of algebraic surfaces. The novel feature of the present exposition is that no assumption on the characteristic of the ground field is assumed.
This requirement calls for exploring the geometry of such surfaces by purely geometric and arithmetic methods that do not rely on transcendental methods such as the theory of periods of algebraic surfaces of type K3, which are close relatives of Enriques surfaces.
Some of the methods use many technical tools from algebraic geometry that are discussed in Volume 1 and may be a useful source of references for the study of algebraic surfaces over fields of positive characteristic. Volume 1 also contains a detailed exposition of the theory of elliptic surfaces over fields of arbitrary characteristic.
The first volume is an essential and greatly extended revision of Enriques Surfaces I, published in 1989 by Birkhäuser and co-authored by F. Cossec and I. Dolgachev. Included is a new chapter devoted to the theory of moduli of Enriques surfaces.
The two volumes together contain many examples and an extensive bibliography made up of more than 700 items.
MoreTable of Contents:
0 Preliminaries.- 1 Enriques surfaces: generalities.- 2 Linear Systems on Enriques Surfaces.- 3 Projective Models of Enriques Surfaces.- 4 Genus One Fibrations.- 5 Moduli Spaces.- Appendix A: Automorphic Forms and Moduli Spaces by S. Kondo.
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