K3 Surfaces and Their Moduli [Paperback]

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 same time, the theory of irreducible holomorphicsymplectic varieties, the higher dimensional analogues of K3 surfaces, hasbecome a mainstream topic in algebraic geometry.

Contributors:S. Boissi?re, 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 Boissi?re, Andrea Cattaneo, MarcNieper-Wisskirchen, and Alessandra Sarti: The automorphism group of theHilbert scheme of two points on a generic projective K3 surface.- Igor Dolgachev: Orbital counting ofcurves on algebraic surfaces and sphere packings.- V. Gritsenko and K. Hulek: Moduli of polarized Enriques surfaces.- Brendan Hassett and Yuri Tls+