Birational Geometry of Hypersurfaces: Gargnano del Garda, Italy, 2018 (Lecture Notes of the Unione Matematica Italiana)
Andreas Hochenegger, "Birational Geometry of Hypersurfaces: Gargnano del Garda, Italy, 2018 (Lecture Notes of the Unione Matematica Italiana) "
English, French | ISBN: 3030186377 | 2019 | 297 pages | EPUB, PDF | 14 MB + 5 MB
English, French | ISBN: 3030186377 | 2019 | 297 pages | EPUB, PDF | 14 MB + 5 MB
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.