Editors:
- 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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Table of contents (7 chapters)
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Front Matter
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Birational Invariants and (Stable) Rationality
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Front Matter
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Hypersurfaces
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Front Matter
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Back Matter
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.
Editors and Affiliations
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Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy
Andreas Hochenegger, Paolo Stellari
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Institut für Mathematik, Johannes Gutenberg Universität Mainz, Mainz, Germany
Manfred Lehn
Bibliographic Information
Book Title: Birational Geometry of Hypersurfaces
Book Subtitle: Gargnano del Garda, Italy, 2018
Editors: Andreas Hochenegger, Manfred Lehn, Paolo Stellari
Series Title: Lecture Notes of the Unione Matematica Italiana
DOI: https://doi.org/10.1007/978-3-030-18638-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Softcover ISBN: 978-3-030-18637-1Published: 17 October 2019
eBook ISBN: 978-3-030-18638-8Published: 08 October 2019
Series ISSN: 1862-9113
Series E-ISSN: 1862-9121
Edition Number: 1
Number of Pages: IX, 297
Number of Illustrations: 36 b/w illustrations
Topics: Algebraic Geometry, Category Theory, Homological Algebra