K3 Surfaces and Their Moduli

This bookprovides an overview of the latest developments concerning the moduli of K3surfaces. It is aimed at algebraic geometers, but is also of interest to numbertheorists and theoretical physicists, and continues the tradition of relatedvolumes like "The Moduli Space of Curves" and "Moduli of Abelian Varieties,"which originated from conferences on the islands Texel and Schiermonnikoog andwhich have become classics.

K3 surfacesand their moduli form a central topic in algebraic geometry and arithmeticgeometry, and have recently attracted a lot of attention from bothmathematicians and theoretical physicists. Advances in this field often resultfrom mixing sophisticated techniques from algebraic geometry, lattice theory, number theory, and dynamical systems. The topic has received significantimpetus due to recent breakthroughs on the Tate conjecture, the study ofstability conditions and derived categories, and links with mirror symmetry andstring theory. At the sametime, the theory of irreducible holomorphicsymplectic varieties, the higher dimensional analogues of K3 surfaces, hasbecome a mainstream topic in algebraic geometry.

Contributors:S. Boissière, A. Cattaneo, I. Dolgachev, V. Gritsenko, B. Hassett, G. Heckman, K. Hulek, S. Katz, A. Klemm, S. Kondo, C. Liedtke, D. Matsushita, M. Nieper-Wisskirchen, G. Oberdieck, K. Oguiso, R. Pandharipande, S. Rieken, A. Sarti, I. Shimada, R. P. Thomas, Y. Tschinkel, A. Verra, C. Voisin.

Introduction. -

Samuel Boissière, Andrea Cattaneo, Marc
Nieper-Wisskirchen, and Alessandra Sarti
: The automorphism group of the
Hilbert scheme of two points on a generic projective K3 surface. -
Igor Dolgachev
: Orbital counting of
curves on algebraic surfaces and sphere packings. -
V. Gritsenko and K. Hulek
: Moduli of polarized Enriques surfaces. -
Brendan Hassett and Yuri Tschinkel
: Extremal
rays and automorphisms of holomorphic symplectic varieties. -
Gert Heckman and Sander Rieken
: An odd
presentation for W(E_6). -
S. Katz, A.
Klemm, and R. Pandharipande, with an appendix by R. P. Thomas
: On the
motivic stable pairs invariants of K3 surfaces. -
Shigeyuki Kondö
: The Igusa quartic and Borcherds products. -
Christian Liedtke
: Lectures on
supersingular K3 surfaces and the crystalline Torelli theorem. -
Daisuke Matsushita
: On deformations of
Lagrangian fibrations. -
G. Oberdieck and
R. Pandharipande
: Curve counting on K3 x E, the Igusa cusp form X_10, and
descendent integration. -
Keiji Oguiso
:
Simple abelian varieties and primitive automorphisms of null entropy of
surfaces. -
Ichiro Shimada
: The
automorphism groups of certain singular K3 surfaces and an Enriques surface. -
Alessandro Verra
: Geometry of genus 8
Nikulin surfaces and rationality of their moduli. -
Claire Voisin
: Remarks and questions on coisotropic subvarieties
and 0-cycles of hyper-Kähler varieties.