The Geometry of Cubic Hypersurfaces

Daniel Huybrechts

458 pages, parution le 28/06/2023

Ajouter à une liste

Indisponible

Résumé

This detailed introduction to cubic hypersurfaces and all the techniques needed to study them leads the reader from classical topics to recent developments studying four-dimensional cubic hypersurfaces. With exercises and careful references to the wider literature, this is an ideal text for graduate students and researchers in algebraic geometry.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.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.Daniel Huybrechts is Professor in the Mathematical Institute of the University of Bonn. He previously held positions at Universite 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).

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Daniel Huybrechts
Parution	28/06/2023
Nb. de pages	458
EAN13	9781009280006

Avantages Eyrolles.com

Livraison à partir de 0,01 € en France métropolitaine

Paiement en ligne SÉCURISÉ

Livraison dans le monde

Retour sous 15 jours

+ d'un million et demi de livres disponibles

The Geometry of Cubic Hypersurfaces

Résumé

Caractéristiques techniques

Consultez aussi