The minimal resolutions of double points in P^1 x P^1 with ACM support
Commutative Algebra
2007-05-23 v2 Algebraic Geometry
Abstract
Let Z be a finite set of double points in P^1 x P^1 and suppose further that X, the support of Z, is arithmetically Cohen-Macaulay (ACM). We present an algorithm, which depends only upon a combinatorial description of X, for the bigraded Betti numbers of I_Z, the defining ideal of Z. We then relate the total Betti numbers of I_Z to the shifts in the graded resolution, thus answering a special case of a question of T. Roemer.
Keywords
Cite
@article{arxiv.math/0609564,
title = {The minimal resolutions of double points in P^1 x P^1 with ACM support},
author = {Elena Guardo and Adam Van Tuyl},
journal= {arXiv preprint arXiv:math/0609564},
year = {2007}
}
Comments
20 pages; revised version includes more detailed proofs in Section 4, and a new section (Section 6) where we answer a special case of question of T. Roemer. To appear J. Pure Appl. Alg