ENGLISH

The Geometry of Cubic Hypersurfaces

By Daniel Huybrechts

Book information

Publisher
Cambridge University Press
Year
2023
ISBN
1009280007, 9781009280006
Language
english
Format
PDF
Filesize
3 MB (3078826 bytes)
Series
Cambridge Studies in Advanced Mathematics, 206
Pages
459\461
Time added
2023-06-25 20:36:51

Description

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.

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