The geometry of Hilbert functions
Commutative Algebra
2007-05-23 v1 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.math/0502145,
title = {The geometry of Hilbert functions},
author = {Juan C. Migliore},
journal= {arXiv preprint arXiv:math/0502145},
year = {2007}
}
Comments
27 pages; expository paper