The geometry of cubic hypersurfaces
著者
書誌事項
The geometry of cubic hypersurfaces
（Cambridge studies in advanced mathematics, 206）
Cambridge University Press, 2023
- : hardback
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注記
Includes bibliographical references (p. 407-433) and index
内容説明・目次
内容説明
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.
目次
- 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.
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