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.
Author(s): Valery Alexeev, Viacheslav V. Nikulin
Series: Mathematical Society of Japan Memoirs, 15
Publisher: The Mathematical Society of Japan
Year: 2006
Language: English
Pages: 149
Title and Copyright Pages.pdf
Foreword
Del Pezzo and K3 surfaces
Foreword
Contents
Del Pezzo and K3 surfaces
Contents
List of Notations
List of Tables
Introduction
Del Pezzo and K3 surfaces
Introduction
Chapter 1. Log del Pezzo Surfaces of Index≤2 and Smooth Divisor Theorem
Del Pezzo and K3 surfaces
Log del Pezzo surfaces ...
Theorem 1.2 ...
Theorem 1.5. ...
Chapter 2. General Theory of DPN Surfaces and K3 Surfaces with Non-Symplectic Involution
Del Pezzo and K3 surfaces
General Theory of DPN ...
Chapter 3. DPN Surfaces of Elliptic Type
Del Pezzo and K3 surfaces
DPN surfaces of elliptic ...
Theorem 3.5. ...
Theorem 3.6 ...
Theorem 3.20. ...
Chapter 4. Classification of Log del Pezzo Surfaces of Index≤2 and Applications
Del Pezzo and K3 surfaces
Classification of log ...
Theorem 4.1. ...
Theorem 4.2. ...
Theorem 4.3. ...
Theorem 4.4. ...
Appendix
Del Pezzo and K3 surfaces
Appendix
Theorem A.l. ...
Theorem A.5. ...
Theorem A.7. ...
Theorem A.8. ...
Theorem A.9. ...
References
Del Pezzo and K3 surfaces
References
Index
