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© 2016

K3 Surfaces and Their Moduli

  • Carel Faber
  • Gavril Farkas
  • Gerard van der Geer

Benefits

  • unique and up-to-date source on the developments in this very active and

  • Connects to other current topics: the study of derived categories and stability conditions, Gromov-Witten theory, and dynamical systems

  • Complements related volumes like “The Moduli Space of Curves” and “Moduli of Abelian Varieties” that have become classics

Book

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

Table of contents

About this book

Introduction

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.

Keywords

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

Bibliographic information

  • Book Title K3 Surfaces and Their Moduli
  • Editors Carel Faber
    Gavril Farkas
    Gerard van der Geer
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI https://doi.org/10.1007/978-3-319-29959-4
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-29958-7
  • Softcover ISBN 978-3-319-80696-9
  • eBook ISBN 978-3-319-29959-4
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages IX, 399
  • Number of Illustrations 11 b/w illustrations, 3 illustrations in colour
  • Topics Algebraic Geometry
  • Buy this book on publisher's site
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