The geometry of cubic hypersurfaces
Author(s)
Bibliographic Information
The geometry of cubic hypersurfaces
（Cambridge studies in advanced mathematics, 206）
Cambridge University Press, 2023
- : hardback
Available at / 24 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
Includes bibliographical references (p. 407-433) and index
Description and Table of Contents
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.
Table of Contents
- 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.
by "Nielsen BookData"