Resolutions of small sets of fat points
Commutative Algebra
2007-05-23 v2 Algebraic Geometry
Abstract
We investigate the minimal graded free resolutions of ideals of at most n+1 fat points in general position in P^n. Our main theorem is that these ideals are componentwise linear. This result yields a number of corollaries, including the multiplicity conjecture of Herzog, Huneke, and Srinivasan in this case. On the computational side, using an iterated mapping cone process, we compute formulas for the graded Betti numbers of ideals associated to two fat points in P^n, verifying a conjecture of Fatabbi, and at most n+1 general double points in P^n.
Keywords
Cite
@article{arxiv.math/0411020,
title = {Resolutions of small sets of fat points},
author = {Christopher Francisco},
journal= {arXiv preprint arXiv:math/0411020},
year = {2007}
}
Comments
15 pages; very minor revisions plus some additional references; to appear in JPAA