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K3 Surfaces and Their Moduli

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  • © 2016

Overview

Editors:
  1. Carel Faber

    1. Mathematisch Instituut, Universiteit Utrecht, Utrecht, The Netherlands

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  2. Gavril Farkas

    1. Institut für Mathematik, Humboldt Universität Berlin, Berlin, Germany

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  3. Gerard van der Geer

    1. Korteweg-de Vries Instituut, Universiteit van Amsterdam, Amsterdam, The Netherlands

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  • 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

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

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-ix
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  2. The Automorphism Group of the Hilbert Scheme of Two Points on a Generic Projective K3 Surface

    • Samuel Boissiére, Andrea Cattaneo, Marc Nieper-Wisskirchen, Alessandra Sarti
    Pages 1-15

  3. Orbital Counting of Curves on Algebraic Surfaces and Sphere Packings

    • Igor Dolgachev
    Pages 17-53

  4. Moduli of Polarized Enriques Surfaces

    • V. Gritsenko, K. Hulek
    Pages 55-72

  5. Extremal Rays and Automorphisms of Holomorphic Symplectic Varieties

    • Brendan Hassett, Yuri Tschinkel
    Pages 73-95

  6. An Odd Presentation for W(E6)

    • Gert Heckman, Sander Rieken
    Pages 97-110

  7. On the Motivic Stable Pairs Invariants of K3 Surfaces

    • S. Katz, A. Klemm, R. Pandharipande, R. P. Thomas
    Pages 111-146

  8. The Igusa Quartic and Borcherds Products

    • Shigeyuki Kondō
    Pages 147-170

  9. Lectures on Supersingular K3 Surfaces and the Crystalline Torelli Theorem

    • Christian Liedtke
    Pages 171-235

  10. On Deformations of Lagrangian Fibrations

    • Daisuke Matsushita
    Pages 237-243

  11. Curve Counting on K3 × E, The Igusa Cusp Form χ10, and Descendent Integration

    • G. Oberdieck, R. Pandharipande
    Pages 245-278

  12. Simple Abelian Varieties and Primitive Automorphisms of Null Entropy of Surfaces

    • Keiji Oguiso
    Pages 279-296

  13. The Automorphism Groups of Certain Singular K3 Surfaces and an Enriques Surface

    • Ichiro Shimada
    Pages 297-343

  14. Geometry of Genus 8 Nikulin Surfaces and Rationality of their Moduli

    • Alessandro Verra
    Pages 345-364

  15. Remarks And Questions On Coisotropic Subvarieties and 0-Cycles of Hyper-Kähler Varieties

    • Claire Voisin
    Pages 365-399
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Keywords

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 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.

Editors and Affiliations

  • Mathematisch Instituut, Universiteit Utrecht, Utrecht, The Netherlands

    Carel Faber

  • Institut für Mathematik, Humboldt Universität Berlin, Berlin, Germany

    Gavril Farkas

  • Korteweg-de Vries Instituut, Universiteit van Amsterdam, Amsterdam, The Netherlands

    Gerard van der Geer

Bibliographic Information

  • Book Title: K3 Surfaces and Their Moduli

  • Editors: Carel Faber, Gavril Farkas, Gerard van der Geer

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-29959-4

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Hardcover ISBN: 978-3-319-29958-7Published: 03 May 2016

  • Softcover ISBN: 978-3-319-80696-9Published: 27 May 2018

  • eBook ISBN: 978-3-319-29959-4Published: 22 April 2016

  • 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

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