Betti numbers of determinantal ideals

[摘要] Let R = k[x(1),...., X-n] be a polynomial ring and let I C R be a graded ideal. In [T. Romer, Betti numbers and shifts in minimal graded free resolutions, arXiv: AC/070119], Romer asked whether under the Cohen-Macaulay assumption the ith Betti number beta(i) (R/I) can be bounded above by a function of the maximal shifts in the minimal graded free R-resolution of R/I as well as bounded below by a function of the minimal shifts. The goal of this paper is to establish such bounds for graded Cohen-Macaulay algebras k[x(1),..., x(n)]/I when I is a standard determinantal ideal of arbitrary codimension. We also discuss other examples as well as when these bounds are sharp. (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-15

[关键词] Betti numbers;determinantal ideals;resolution