Ja n 20 07 BETTI NUMBERS OF DETERMINANTAL IDEALS ROSA
نویسنده
چکیده
Let R = k[x 1 , · · · , x n ] be a polynomial ring and let I ⊂ R be a graded ideal. In [16], Römer asked whether under the Cohen-Macaulay assumption the i-th Betti number β 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.
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