Ebook: Birational Geometry of Hypersurfaces: Gargnano del Garda, Italy, 2018
- Tags: Mathematics, Algebraic Geometry, Category Theory Homological Algebra
- Series: Lecture Notes of the Unione Matematica Italiana 26
- Year: 2019
- Publisher: Springer International Publishing
- Edition: 1st ed. 2019
- Language: English-French
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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.