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Hilbert functions and geometry

Fabre Bruno
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Abstract

This note is devoted to the study of the links between the Hilbert function of a subscheme X of the projective space, and its geometric properties. We will assume that X is arithmetically Cohen-Macaulay, which allows us to characterize its Hilbert function by a d integers, where d is the degree of X. We study in this context the geometric description of special linear systems of dimension maximal with respect to their degree on projective Gorenstein curves.

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Fabre Bruno. 2004-04-13. Hilbert functions and geometry. https://arxiv.org/abs/math/0404138

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