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On the postulation of 0-dimensional subschemes on a smooth quadric. (English) Zbl 0723.14035
If X is a 0-dimensional subscheme of a smooth quadric $$Q\cong {\mathbb{P}}^ 1\times {\mathbb{P}}^ 1$$ we investigate the behaviour of X with respect to the linear systems of divisors of any degree (a,b). This leads to the construction of a matrix of integers which plays the role of a Hilbert function of X; we study numerical properties of this matrix and their connection with the geometry of X. Further we put into relation the graded Betti numbers of a minimal free resolution of X on Q with that matrix, and give a complete description of the arithmetically Cohen- Macaulay 0-dimensional subschemes of Q.
Reviewer: S.Giuffrida

##### MSC:
 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) 14N05 Projective techniques in algebraic geometry 13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
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