The Geometry of Cubic Hypersurfaces

Inbunden, Engelska, 2023

Del 206 i serien Cambridge Studies in Advanced Mathematics

913 kr

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Beskrivning

Cubic hypersurfaces are described by almost the simplest possible polynomial equations, yet their behaviour is rich enough to demonstrate many of the central challenges in algebraic geometry. With exercises and detailed references to the wider literature, this thorough text introduces cubic hypersurfaces and all the techniques needed to study them. The book starts by laying the foundations for the study of cubic hypersurfaces and of many other algebraic varieties, covering cohomology and Hodge theory of hypersurfaces, moduli spaces of those and Fano varieties of linear subspaces contained in hypersurfaces. The next three chapters examine the general machinery applied to cubic hypersurfaces of dimension two, three, and four. Finally, the author looks at cubic hypersurfaces from a categorical point of view and describes motivic features. Based on the author's lecture courses, this is an ideal text for graduate students as well as an invaluable reference for researchers in algebraic geometry.

Produktinformation

Utgivningsdatum:2023-06-29
Mått:159 x 235 x 32 mm
Vikt:830 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Studies in Advanced Mathematics
Antal sidor:460
Förlag:Cambridge University Press
ISBN:9781009280006

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Mer om författaren

Daniel Huybrechts is Professor in the Mathematical Institute of the University of Bonn. He previously held positions at Université Denis Diderot Paris 7 and the University of Cologne. He has published five books, including 'Lectures on K3 Surfaces' (2016) and 'Fourier-Mukai Transforms in Algebraic Geometry' (2006).

Recensioner i media

'What a beautiful book. Several turning points in algebraic geometry have in their background a cubic hypersurface. This superb exposition, by one of the masters in the field, takes the reader, in a friendly manner, through the fascinating, and occasionally mysterious, properties of these geometrical objects, and through them offers a glimpse of the underlying Hodge theory, of the theory of periods, the theory of motives, and the theory of derived categories. Graduate students, researchers, and colleagues will all find this unified treatment of cubic hypersurfaces profoundly inspiring.' Enrico Arbarello, Accademia Nazionale dei Lincei

Innehållsförteckning

1. Basic facts; 2. Fano varieties of lines; 3. Moduli spaces; 4. Cubic surfaces; 5. Cubic threefolds; 6. Cubic fourfolds; 7. Derived categories of cubic hypersurfaces; References; Subject index.