Birational Geometry of Hypersurfaces

Gargnano del Garda, Italy, 2018

  • Andreas Hochenegger
  • Manfred Lehn
  • Paolo Stellari

Part of the Lecture Notes of the Unione Matematica Italiana book series (UMILN, volume 26)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Birational Invariants and (Stable) Rationality

    1. Front Matter
      Pages 1-1
    2. Jean-Louis Colliot-Thélène
      Pages 73-110
    3. Jean-Louis Colliot-Thélène
      Pages 111-125
  3. Hypersurfaces

  4. Back Matter
    Pages 297-297

About this book


Originating from the School on Birational Geometry of Hypersurfaces, this volume focuses on the notion of (stable) rationality of projective varieties and, more specifically, hypersurfaces in projective spaces, and provides a large number of open questions, techniques and spectacular results.

The aim of the school was to shed light on this vast area of research by concentrating on two main aspects: (1) Approaches focusing on (stable) rationality using deformation theory and Chow-theoretic tools like decomposition of the diagonal; (2) The connection between K3 surfaces, hyperkähler geometry and cubic fourfolds, which has both a Hodge-theoretic and a homological side.

Featuring the beautiful lectures given at the school by Jean-Louis Colliot-Thélène, Daniel Huybrechts, Emanuele Macrì, and Claire Voisin, the volume also includes additional notes by János Kollár and an appendix by Andreas Hochenegger.



14-06,14E08,16E35,14D22,14C30 Algebraic Geometry Rational Varieties Cubic Fourfolds Derived Categories K3 Surfaces

Editors and affiliations

  • Andreas Hochenegger
    • 1
  • Manfred Lehn
    • 2
  • Paolo Stellari
    • 3
  1. 1.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanoItaly
  2. 2.Institut für MathematikJohannes Gutenberg Universität MainzMainzGermany
  3. 3.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanoItaly

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