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Birational geometry of hypersurfaces : gargnano del garda, italy, 2018 [Documento eletrónico] / edited by Andreas Hochenegger, Manfred Lehn, Paolo Stellari. - Cham : Springer International Publishing : Springer , 2019 . - IX, 297 p. : il.. - (Lecture Notes of the Unione Matematica Italiana) ; 26 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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ISBN 978-3-030-18638-8

Algebraic geometry
Algebra, Homological

LCC QA564-609