Powers of Complete Intersections: Graded Betti Numbers and Applications
نویسنده
چکیده
Abstract. Let I = (F1, . . . , Fr) be a homogeneous ideal of the ring R = k[x0, . . . , xn] generated by a regular sequence of type (d1, . . . , dr). We give an elementary proof for an explicit description of the graded Betti numbers of Is for any s ≥ 1. These numbers depend only upon the type and s. We then use this description to: (1) write HR/Is , the Hilbert function of R/Is, in terms of HR/I ; (2) verify that the kalgebra R/Is satisfies a conjecture of Herzog-Huneke-Srinivasan; and (3) obtain information about the numerical invariants associated to sets of fat points in Pn whose support is a complete intersection or a complete intersection minus a point.
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