@article{915871, recid = {915871}, author = {Hochenegger, Andreas, and Lehn, Manfred, and Stellari, Paolo,}, title = {Birational geometry of hypersurfaces : Gargnano del Garda, Italy, 2018 /}, pages = {1 online resource (ix, 297 pages) :}, abstract = {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.}, url = {http://library.usi.edu/record/915871}, doi = {https://doi.org/10.1007/978-3-030-18638-8}, }