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Titlebook: Birational Geometry of Hypersurfaces; Gargnano del Garda, Andreas Hochenegger,Manfred Lehn,Paolo Stellari Book 2019 Springer Nature Switze

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期刊全称Birational Geometry of Hypersurfaces
期刊简称Gargnano del Garda,
影响因子2023Andreas Hochenegger,Manfred Lehn,Paolo Stellari
视频video
发行地址Describes the most intriguing Hodge-theoretic aspects of cubic fourfolds.Presents well-written surveys by leading experts on recent developments on rationality questions for hypersurfaces.Provides a c
学科分类Lecture Notes of the Unione Matematica Italiana
图书封面Titlebook: Birational Geometry of Hypersurfaces; Gargnano del Garda,  Andreas Hochenegger,Manfred Lehn,Paolo Stellari Book 2019 Springer Nature Switze
影响因子.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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https://doi.org/10.1007/978-3-030-18638-814-06,14E08,16E35,14D22,14C30; Algebraic Geometry; Rational Varieties; Cubic Fourfolds; Derived Categori
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Hodge Theory of Cubic Fourfolds, Their Fano Varieties, and Associated K3 Categoriesge structures that come naturally associated with a cubic fourfold. The emphasis is on the Hodge and lattice theoretic aspects with many technical details worked out explicitly. More geometric or derived results are only hinted at.
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https://doi.org/10.1007/978-3-658-40109-2o distinguish (stably) rational varieties from general unirational varieties. In particular, we study the notion of Chow or cohomological decomposition of the diagonal, which is a necessary criterion for stable rationality. Having better stability properties than the previously known obstructions un
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