Carel Faber Livres

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.

Abelian varieties and their moduli are a central topic of increasing importance in today`s mathematics. Applications range from algebraic geometry and number theory to mathematical physics. The present collection of 17 refereed articles originates from the third „Texel Conference“ held in 1999. Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field. The book will appeal to pure mathematicians, especially algebraic geometers and number theorists, but will also be relevant for researchers in mathematical physics.

The Dutch Intercity Seminar on Moduli, which dates back to the early eighties, was an initiative of G. van der Geer, F. Oort and C. Peters. Through the years it became a focal point of Dutch mathematics and it gained some fame, also outside Holland, as an active biweekly research seminar. The tradition continues up to today. The present volume, with contributions of R. Dijkgraaf, C. Faber, G. van der Geer, R. Hain, E. Looijenga, and F. Oort, originates from the seminar held in 1995--96. Some of the articles here were discussed, in preliminary form, in the seminar; others are completely new. Two introductory papers, on moduli of abelian varieties and on moduli of curves, accompany the articles.