Presents a unique and up-to-date source on the developments in this very active and diverse field
Connects to other current topics: the study of derived categories and stability conditions, Gromov-Witten theory, and dynamical systems
Complements related volumes like “The Moduli Space of Curves” and “Moduli of Abelian Varieties” that have become classics
This book provides an overview of the latest developments concerning the moduli of K3 surfaces. It is aimed at algebraic geometers, but is also of interest to number theorists and theoretical physicists, and continues the tradition of related volumes like “The Moduli Space of Curves” and “Moduli of Abelian Varieties,” which originated from conferences on the islands Texel and Schiermonnikoog and which have become classics.
K3 surfaces and their moduli form a central topic in algebraic geometry and arithmetic geometry, and have recently attracted a lot of attention from both mathematicians and theoretical physicists. Advances in this field often result from mixing sophisticated techniques from algebraic geometry, lattice theory, number theory, and dynamical systems. The topic has received significant impetus due to recent breakthroughs on the Tate conjecture, the study of stability conditions and derived categories, and links with mirror symmetry and string theory. At the same time, the theory of irreducible holomorphic symplectic varieties, the higher dimensional analogues of K3 surfaces, has become a mainstream topic in algebraic geometry.
Topics
Algebraic Geometry
Author(s): Carel Faber, Gavril Farkas, Gerard van der Geer
Series: Progress in Mathematics 315
Edition: 1
Publisher: Birkhäuser
Year: 2016
Language: English
Pages: C,X,399
Tags: Algebraic Geometry
Front Matter....Pages i-ix
The Automorphism Group of the Hilbert Scheme of Two Points on a Generic Projective K3 Surface....Pages 1-15
Orbital Counting of Curves on Algebraic Surfaces and Sphere Packings....Pages 17-53
Moduli of Polarized Enriques Surfaces....Pages 55-72
Extremal Rays and Automorphisms of Holomorphic Symplectic Varieties....Pages 73-95
An Odd Presentation for W(E6)....Pages 97-110
On the Motivic Stable Pairs Invariants of K3 Surfaces....Pages 111-146
The Igusa Quartic and Borcherds Products....Pages 147-170
Lectures on Supersingular K3 Surfaces and the Crystalline Torelli Theorem....Pages 171-235
On Deformations of Lagrangian Fibrations....Pages 237-243
Curve Counting on K3 × E, The Igusa Cusp Form χ10, and Descendent Integration....Pages 245-278
Simple Abelian Varieties and Primitive Automorphisms of Null Entropy of Surfaces....Pages 279-296
The Automorphism Groups of Certain Singular K3 Surfaces and an Enriques Surface....Pages 297-343
Geometry of Genus 8 Nikulin Surfaces and Rationality of their Moduli....Pages 345-364
Remarks And Questions On Coisotropic Subvarieties and 0-Cycles of Hyper-Kähler Varieties....Pages 365-399
