K3 Surfaces and Their Moduli

  • Carel Faber
  • Gavril Farkas
  • Gerard van der Geer

Part of the Progress in Mathematics book series (PM, volume 315)

Table of contents

About this book


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 same time, 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.


K3 surface moduli space holomorphic symplectic varieties algebraic geometry arithmetic geometry

Editors and affiliations

  • Carel Faber
    • 1
  • Gavril Farkas
    • 2
  • Gerard van der Geer
    • 3
  1. 1.Mathematisch InstituutUniversiteit UtrechtUtrechtThe Netherlands
  2. 2.Institut für MathematikHumboldt Universität BerlinBerlinGermany
  3. 3.Korteweg-de Vries InstituutUniversiteit van AmsterdamAmsterdamThe Netherlands

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