Powers of complete intersections: graded Betti numbers and applications

By Elena Guardo, Adam Van Tuyl. 2004

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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 I s 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 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

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/bfb3a291da8138c91a1e55c79a3cb78bf9a5b991

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In Algebra and Number Theory

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In Discrete Mathematics and Combinatorics

Citations in the corpus

On the first infinitesimal neighborhood of a linear configuration of points in P2 (2006, background): “it turns out that for the special h’s covered by the work of Id`a [44], or Buckles, Guardo and VanTuyl [8], [9] and [ 36 ], the elements they construct in D(h) and BettiD(h) are usually dierent from the elements we have constructed (see e.g.”
Betti numbers of graded modules and the Multiplicity Conjecture in the non-Cohen-Macaulay case (2008, background): “In a series of papers [Srinivasan 1998; Gold 2003; Guardo and Van Tuyl 2005; Migliore et al. 2005; 2008b; Römer 2005; Francisco 2006; Herzog and Zheng 2006; Kubitzke and Welker 2006; Miró-Roig 2006; Francisco and Van Tuyl 2007; Gold et al. 2007; Seo and Srinivasan 2007; Zanello 2007; Goff 2008; Hibi”