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Powers of complete intersections: graded Betti numbers and applications | | Elena Guardo
; Adam Van Tuyl
; | | Date: |
6 Sep 2004 | | Subject: | Commutative Algebra; Algebraic Geometry MSC-class: 13D40; 13D02; 13H10; 14A15 | math.AC math.AG | | Affiliation: | Catania) and Adam Van Tuyl (Lakehead | | Abstract: | Let I = (F_1,...,F_r) be a homogeneous ideal of R = k[x_0,...,x_n] generated by a regular sequence of type (d_1,...,d_r). We give an elementary proof for an explicit description of the graded Betti numbers of I^s for any s geq 1. These numbers depend only upon the type and s. We then use this description to: (1) write H_{R/I^s}, the Hilbert function of R/I^s, in terms of H_{R/I}; (2) verify that the k-algebra R/I^s satisfies a conjecture of Herzog-Huneke-Srinivasan; and (3) obtain information about the numerical invariants associated to sets of fat points in P^n whose support is a complete intersection or a complete intersection minus a point. | | Source: | arXiv, math.AC/0409090 | | Services: | Forum | Review | PDF | Favorites | |
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