03055nam 22005655 450 991034931840332120200703045420.03-030-18638-510.1007/978-3-030-18638-8(CKB)4100000009453334(DE-He213)978-3-030-18638-8(MiAaPQ)EBC5928979(PPN)258304103(EXLCZ)99410000000945333420191008d2019 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierBirational Geometry of Hypersurfaces Gargnano del Garda, Italy, 2018 /edited by Andreas Hochenegger, Manfred Lehn, Paolo Stellari1st ed. 2019.Cham :Springer International Publishing :Imprint: Springer,2019.1 online resource (IX, 297 p. 36 illus.) Lecture Notes of the Unione Matematica Italiana,1862-9113 ;263-030-18637-7 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. .Lecture Notes of the Unione Matematica Italiana,1862-9113 ;26Algebraic geometryCategory theory (Mathematics)Homological algebraAlgebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019Category Theory, Homological Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11035Algebraic geometry.Category theory (Mathematics).Homological algebra.Algebraic Geometry.Category Theory, Homological Algebra.516.35516.5Hochenegger Andreasedthttp://id.loc.gov/vocabulary/relators/edtLehn Manfrededthttp://id.loc.gov/vocabulary/relators/edtStellari Paoloedthttp://id.loc.gov/vocabulary/relators/edtMiAaPQMiAaPQMiAaPQBOOK9910349318403321Birational Geometry of Hypersurfaces1668178UNINA