A pr 2 00 7 THE MINIMAL RESOLUTIONS OF DOUBLE POINTS IN P 1 × P 1 WITH ACM SUPPORT
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چکیده
Let Z be a finite set of double points in P 1 × 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 Römer.
منابع مشابه
Se p 20 06 THE MINIMAL RESOLUTIONS OF DOUBLE POINTS IN P 1 × P 1 WITH ACM SUPPORT
Let Z be a finite set of double points in P 1 × P 1 and suppose further that X, the support of Z, is arithmetically Cohen-Macaulay (ACM). The scheme Z is rarely ACM. In this note 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.
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