Birational Geometry Of Hypersurfaces: Gargnano Del Garda, Italy, 2018
by Andreas Hochenegger /
2019 / English / PDF
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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, hyperkhler 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-Thlne, Daniel Huybrechts, Emanuele Macr, and Claire Voisin, the volume also includes additional notes by Jnos Kollr and an appendix by Andreas Hochenegger.
