by Valery Alexeev (University of Georgia, USA) & Viacheslav V Nikulin (University of Liverpool, UK & Steklov Institute of Mathematics, Russia)

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.

Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets

• Log del Pezzo Surfaces of Index ≤ 2 and Smooth Divisor Theorem
• General Theory of DPN Surfaces and K3 Surfaces with Non-Symplectic Involution
• DPN Surfaces of Elliptic Type
• Classification of Log del Pezzo Surfaces of Index ≤ 2 and Applications
• Appendices:
  • Integral Symmetric Bilinear Forms. Elements of the Discriminant Forms Technique
  • Classification of Main Invariants and Their Geometric Interpretation
  • The Analogue of Witt's Theorem for 2-Elementary Finite Forms
  • Calculations of Fundamental Chambers