The geometry of Hilbert functions

Details The geometry of Hilbert functions The geometry of Hilbert functions

2005-02-07

arxiv.org/abs/math/0502145v1

Mathematics

Commutative Algebra

27 pages; expository paper

Scientific paper

We compare and contrast results of E. Davis, of A. Bigatti, A.V. Geramita and the author, and of J. Ahn and the author. The underlying idea is that certain numerical conditions on the Hilbert function of a finite set of points in projective space force geometric consequences on the base loci of the linear systems of hypersurfaces containing the points. When the points have uniform position, this tends to force better behavior for these base loci. However, unexpected behavior is still possible, and we give examples.

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