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 sametime, the theory of irreducible holomorphic
symplectic varieties, the higher dimensional analogues of K3 surfaces, has
become 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.