Powers of complete intersections: graded Betti numbers and applications

Details Powers of complete intersections: graded Betti numbers and applications Powers of complete intersections: graded Betti numbers and applications

2004-09-06

arxiv.org/abs/math/0409090v2

Mathematics

Commutative Algebra

15 pages, minor corrections, to appear in Ill. J. Math

Scientific paper

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.

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