The Geometry of Cubic Hypersurfaces
Language: English Series: Cambridge studies in advanced mathematics ; 206Publication details: New Delhi Cambridge University press 2023Description: xvii, 441pISBN: 9781009280006(HB)Subject(s): Geometry | Differential geometry | Cubic hypersurface | MathematicsCurrent library | Home library | Call number | Materials specified | Status | Notes | Date due | Barcode |
---|---|---|---|---|---|---|---|
IMSc Library | IMSc Library | 514.75 HUY (Browse shelf (Opens below)) | Not for loan | New Arrivals Displayed Till 30th September 2024 | 78240 |
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327 AND The Secret World : A History of Intelligence | 5 BHA The Man from the Future : The Visionary Life of John von Neumann | 513.83 BRE Sheaf Theory | 514.75 HUY The Geometry of Cubic Hypersurfaces | 514.75 HUY The Geometry of Moduli Spaces of Sheaves | 519.2 BIL Probability and Measure | 53 HEI Physics and Philosophy: The Revolution in Modern Science |
1.Basic
2.Fano variable of lines
3.Moduli spaces
4.Cubic surface
5.Cubic threefolds
6.Cubic fourfolds
7.Derived categories of cubic hypersurface
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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