K3 Surfaces and Their Moduli

Viac o knihe

This book offers an overview of recent advancements in the moduli of K3 surfaces, targeting algebraic geometers while also appealing to number theorists and theoretical physicists. It continues the legacy of previous volumes like “The Moduli Space of Curves” and “Moduli of Abelian Varieties,” which emerged from conferences on Texel and Schiermonnikoog and have become essential references. K3 surfaces and their moduli are pivotal in both algebraic and arithmetic geometry, garnering significant attention from mathematicians and physicists alike. Progress in this area often arises from the integration of advanced techniques from algebraic geometry, lattice theory, number theory, and dynamical systems. Recent developments have been fueled by breakthroughs related to the Tate conjecture, stability conditions, derived categories, and connections to mirror symmetry and string theory. Concurrently, the theory of irreducible holomorphic symplectic varieties, which are higher-dimensional analogues of K3 surfaces, has gained prominence in algebraic geometry. The contributors include notable figures such as S. Boissière, A. Cattaneo, I. Dolgachev, and many others, reflecting a diverse range of expertise in this vibrant field.