2006/09/20 by Elena Guardo, Guardo, Elena, Adam Van Tuyl +1
Mathematics · #13D02 #13D40 #13H10 #14A15 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13D02 #msc:13D40 #msc:13H10 #msc:14A15
paper · pdf · doi:10.48550/arxiv.math/0609564
20 pages; revised version includes more detailed proofs in Section 4, and a new section (Section 6) where we answer a special case of question of T. Roemer. To appear J. Pure Appl. Alg
arxiv created 2007/04/07 · arxiv updated 2009/12/01
Let Z be a finite set of double points in P1 x P1 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 IZ, the defining ideal of Z. We then relate the total Betti numbers of IZ to the shifts in the graded resolution, thus answering a special case of a question of T. Roemer.