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Equations des variétés de Kummer. (French) Zbl 0789.14038

The aim of this paper is to study the equations defining a class of algebraic varieties, namely the class of Kummer varieties. The first result is that we get the degree of the generators of the homogeneous ideal associated to a variety from this class embedded by an ample invertible sheaf normally generated. In the second part we describe explicitly generators of the space of quadrics containing the embedded variety, determining in this way, completely in many cases, the homogeneous ideal.
Reviewer: A.Khaled (Orsay)

MSC:

14J28 \(K3\) surfaces and Enriques surfaces
14A05 Relevant commutative algebra
14K25 Theta functions and abelian varieties
14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
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