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The minimal resolutions of double points in P^1 x P^1 with ACM support

Elena Guardo·Adam Van Tuyl
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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.

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Elena Guardo, Adam Van Tuyl. 2007-04-07. The minimal resolutions of double points in P^1 x P^1 with ACM support. https://arxiv.org/abs/math/0609564

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