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© 2017

Geometry Over Nonclosed Fields

  • Fedor Bogomolov
  • Brendan Hassett
  • Yuri Tschinkel
Conference proceedings

Part of the Simons Symposia book series (SISY)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Fedor Bogomolov, Ljudmila Kamenova, Steven Lu, Misha Verbitsky
    Pages 1-17
  3. Olivier Debarre, Antonio Laface, Xavier Roulleau
    Pages 19-51
  4. Andrew Harder, Ludmil Katzarkov, Yijia Liu
    Pages 53-96
  5. Max Lieblich, Martin Olsson
    Pages 127-156
  6. Anthony Várilly-Alvarado
    Pages 197-248

About these proceedings

Introduction

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. 

Keywords

algebraic geometry rational curves K3 surfaces cubic four-folds hyper-Kahler manifolds

Editors and affiliations

  • Fedor Bogomolov
    • 1
  • Brendan Hassett
    • 2
  • Yuri Tschinkel
    • 3
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Department of MathematicsBrown UniversityProvidenceUSA
  3. 3.Courant Institute of Mathematical Sciences and Simons FoundationNew York UniversityNew YorkUSA

About the editors

Fedor Bogomolov, Courant Institute of Mathematical Sciences, New York, NY
Brendan 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
  • Series Abbreviated Title Simons Symposia
  • DOI https://doi.org/10.1007/978-3-319-49763-1
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-49762-4
  • Softcover ISBN 978-3-319-84235-6
  • eBook ISBN 978-3-319-49763-1
  • 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
  • Buy this book on publisher's site
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