The minimal resolutions of double points in P1 x P1 with ACM support

[摘要] 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 Romer. (c) 2007 Elsevier B.V. All rights reserved.

[发布日期] 2007-12-01