Fano Varieties
Identifieur interne : 000F81 ( Main/Exploration ); précédent : 000F80; suivant : 000F82Fano Varieties
Auteurs : Olivier Debarre [France]Source :
- Bolyai Society Mathematical Studies [ 1217-4696 ] ; 2003.
Abstract
Abstract: There are few objects canonically attached to a smooth projective algebraic variety X of dimension n. One of them is the invertible sheaf of differential n-forms, or equivalently the corresponding divisor class, for which one chooses a representant K X , called a canonical divisor. One can start a classification according to “how ample” K X is, and consider the two extreme classes of varieties: those for which K X is ample, and those for which -K X is ample. Varieties X for which K X is ample are called varieties of general type and, as their name suggests, there are so many of them that a classification is impossible. In contrast, there are “very few” varieties X for which -K X is ample; they are called Fano varieties. In many cases, such as in Mori’s classification program of algebraic varieties known as the Minimal Model Program, it is necessary to allow some kind of singularities, which we describe below.
Url:
DOI: 10.1007/978-3-662-05123-8_5
Affiliations:
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