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Birational Geometry of Hypersurfaces

Gargnano del Garda, Italy, 2018

  • Book
  • © 2019


  • Describes the most intriguing Hodge-theoretic aspects of cubic fourfolds
  • Presents well-written surveys by leading experts on recent developments on rationality questions for hypersurfaces
  • Provides a comprehensive and state-of-the-art introduction to the new and exciting subject of non-commutative K3 surfaces

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

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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.


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Table of contents (7 chapters)

  1. Birational Invariants and (Stable) Rationality

Editors and Affiliations

  • Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy

    Andreas Hochenegger, Paolo Stellari

  • Institut für Mathematik, Johannes Gutenberg Universität Mainz, Mainz, Germany

    Manfred Lehn

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