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Geometry Over Nonclosed Fields

  • Conference proceedings
  • © 2017

Overview

Editors:
  1. Fedor Bogomolov

    1. Courant Institute of Mathematical Sciences, New York University, New York, USA

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  2. Brendan Hassett

    1. Department of Mathematics, Brown University, Providence, USA

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  3. Yuri Tschinkel

    1. Courant Institute of Mathematical Sciences and Simons Foundation, New York University, New York, USA

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  • Covers exciting new research in the fields of classical algebraic geometry and arithmetic geometry
  • Examines recent research and results concerning K3-surfaces, including formulations of the Torelli Theorem for K3-surfaces and the arithmetic of K3-surfaces.
  • Provides students and researchers with fresh discussions of classical, long-standing problems.
  • Includes supplementary material: sn.pub/extras

Part of the book series: Simons Symposia (SISY)

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About this book

Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higher-dimensional generalizations. One main recent insight the book covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of long-standing conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail. 

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Table of contents (8 papers)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. On the Kobayashi Pseudometric, Complex Automorphisms and Hyperkähler Manifolds

    • Fedor Bogomolov, Ljudmila Kamenova, Steven Lu, Misha Verbitsky
    Pages 1-17

  3. Lines on Cubic Hypersurfaces Over Finite Fields

    • Olivier Debarre, Antonio Laface, Xavier Roulleau
    Pages 19-51

  4. Perverse Sheaves of Categories and Non-rationality

    • Andrew Harder, Ludmil Katzarkov, Yijia Liu
    Pages 53-96

  5. Divisor Classes and the Virtual Canonical Bundle for Genus 0 Maps

    • A. J. de Jong, Jason Starr
    Pages 97-126

  6. A Stronger Derived Torelli Theorem for K3 Surfaces

    • Max Lieblich, Martin Olsson
    Pages 127-156

  7. Morphisms to Brauer–Severi Varieties, with Applications to Del Pezzo Surfaces

    • Christian Liedtke
    Pages 157-196

  8. Arithmetic of K3 Surfaces

    • Anthony Várilly-Alvarado
    Pages 197-248

  9. Odd-Dimensional Cohomology with Finite Coefficients and Roots of Unity

    • Yuri G. Zarhin
    Pages 249-261
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Editors and Affiliations

  • Courant Institute of Mathematical Sciences, New York University, New York, USA

    Fedor Bogomolov

  • Department of Mathematics, Brown University, Providence, USA

    Brendan Hassett

  • Courant Institute of Mathematical Sciences and Simons Foundation, New York University, New York, USA

    Yuri Tschinkel

About the editors

Fedor Bogomolov, Courant Institute of Mathematical Sciences, New York, NYBrendan Hassett, Brown University, Providence, Rhode Island
Yuri Tshinkel,Courant Institute of Mathematical Sciences, New York, NY

Bibliographic Information

  • Book Title: Geometry Over Nonclosed Fields

  • Editors: Fedor Bogomolov, Brendan Hassett, Yuri Tschinkel

  • Series Title: Simons Symposia

  • DOI: https://doi.org/10.1007/978-3-319-49763-1

  • Publisher: Springer Cham

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

  • Copyright Information: Springer International Publishing AG 2017

  • Hardcover ISBN: 978-3-319-49762-4Published: 10 February 2017

  • Softcover ISBN: 978-3-319-84235-6Published: 13 July 2018

  • eBook ISBN: 978-3-319-49763-1Published: 09 February 2017

  • Series ISSN: 2365-9564

  • Series E-ISSN: 2365-9572

  • Edition Number: 1

  • Number of Pages: IX, 261

  • Number of Illustrations: 2 b/w illustrations, 1 illustrations in colour

  • Topics: Algebraic Geometry

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