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

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1862-9113 ents on rationality questions for hypersurfaces.Provides a c.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

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https://doi.org/10.1007/978-3-658-40109-2n of the diagonal, which is a necessary criterion for stable rationality. Having better stability properties than the previously known obstructions under specialization with mildly singular central fibers, it has been very useful in the recent study of rationality questions.

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Birational Invariants and Decomposition of the Diagonaln of the diagonal, which is a necessary criterion for stable rationality. Having better stability properties than the previously known obstructions under specialization with mildly singular central fibers, it has been very useful in the recent study of rationality questions.

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Book 2019s 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) rational

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1862-9113 g 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.. . .978-3-030-18637-1978-3-030-18638-8Series ISSN 1862-9113 Series E-ISSN 1862-9121

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Birational Invariants and Decomposition of the Diagonalo 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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Non rationalité stable sur les corps quelconquesand unirationality, R-equivalence on rational points, Chow groups of zero-cycles, Galois action on the Picard group, Brauer group, higher unramified cohomology, global differentials, specialisation method (via R-equivalence), geometrically rational surfaces, cubic hypersurfaces.