The Geometry of Cubic Hypersurfaces
06/2023 · Cambridge Studies in Advanced Mathematics Livro 206 · Cambridge University Press
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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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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).
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