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Simons Symposia

Geometry Over Nonclosed Fields

Editors: Bogomolov, Fedor, Hassett, Brendan, Tschinkel, Yuri (Eds.)

  • 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. 
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Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-319-49763-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-319-49762-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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. 

About the authors

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

Table of contents (8 chapters)

  • On the Kobayashi Pseudometric, Complex Automorphisms and Hyperkähler Manifolds

    Bogomolov, Fedor (et al.)

    Pages 1-17

  • Lines on Cubic Hypersurfaces Over Finite Fields

    Debarre, Olivier (et al.)

    Pages 19-51

  • Perverse Sheaves of Categories and Non-rationality

    Harder, Andrew (et al.)

    Pages 53-96

  • Divisor Classes and the Virtual Canonical Bundle for Genus 0 Maps

    Jong, A. J. (et al.)

    Pages 97-126

  • A Stronger Derived Torelli Theorem for K3 Surfaces

    Lieblich, Max (et al.)

    Pages 127-156

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-319-49763-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-319-49762-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometry Over Nonclosed Fields
Editors
  • Fedor Bogomolov
  • Brendan Hassett
  • Yuri Tschinkel
Series Title
Simons Symposia
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-49763-1
DOI
10.1007/978-3-319-49763-1
Hardcover ISBN
978-3-319-49762-4
Series ISSN
2365-9564
Edition Number
1
Number of Pages
IX, 261
Number of Illustrations and Tables
2 b/w illustrations, 1 illustrations in colour
Topics