Mathematical Society of Japan Memoirs

Del Pezzo and K3 Surfaces

Valery Alexeev and Viacheslav V. Nikulin

Book information

Authors
Valery Alexeev and Viacheslav V. Nikulin

Publication information
MSJ Memoirs, Volume 15
Tokyo, Japan: The Mathematical Society of Japan, 2006
149 pp.

Dates
Publication date: 2006
First available in Project Euclid: 11 December 2014

Permanent link to this book
https://projecteuclid.org/euclid.msjm/1418310898

Digital Object Identifier:
doi:10.2969/msjmemoirs/015010000

ISBN:
978-4-931469-34-1

Zentralblatt MATH:
1097.14001

Mathematical Reviews (MathSciNet):
MR2227002

Subjects
Primary: 14J25: Special surfaces {For Hilbert modular surfaces, see 14G35} 14J26: Rational and ruled surfaces 14J28: $K3$ surfaces and Enriques surfaces
Secondary: 14J17: Singularities [See also 14B05, 14E15] 14J45: Fano varieties 14J50: Automorphisms of surfaces and higher-dimensional varieties 11E12: Quadratic forms over global rings and fields 11F22: Relationship to Lie algebras and finite simple groups 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]

Rights
Copyright © 2006, The Mathematical Society of Japan

Citation
Valery Alexeev and Viacheslav V. Nikulin, Del Pezzo and K3 Surfaces (Tokyo: The Mathematical Society of Japan, 2006)

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Abstract

The present volume is a self-contained exposition on the complete classification of singular del Pezzo surfaces of index one or two. The method of the classification used here depends on the intriguing interplay between del Pezzo surfaces and K3 surfaces, between geometry of exceptional divisors and the theory of hyperbolic lattices. The topics involved contain hot issues of research in algebraic geometry, group theory and mathematical physics.

This book, written by two leading researchers of the subjects, is not only a beautiful and accessible survey on del Pezzo surfaces and K3 surfaces, but also an excellent introduction to the general theory of Q-Fano varieties.