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Spring 2005 Powers of complete intersections: graded Betti numbers and applications
Elena Guardo, Adam Van Tuyl
Illinois J. Math. 49(1): 265-279 (Spring 2005). DOI: 10.1215/ijm/1258138318


Let $I = (F_1,\ldots,F_r)$ be a homogeneous ideal of the ring $R = k[x_0,\ldots,x_n]$ generated by a regular sequence of type $(d_1,\ldots,d_r)$. 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 $\mathbb{P}^n$ whose support is a complete intersection or a complete intersection minus a point.


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Elena Guardo. Adam Van Tuyl. "Powers of complete intersections: graded Betti numbers and applications." Illinois J. Math. 49 (1) 265 - 279, Spring 2005.


Published: Spring 2005
First available in Project Euclid: 13 November 2009

zbMATH: 1089.13008
MathSciNet: MR2157379
Digital Object Identifier: 10.1215/ijm/1258138318

Primary: 13D40
Secondary: 13D02 , 13H10 , 14A15

Rights: Copyright © 2005 University of Illinois at Urbana-Champaign


Vol.49 • No. 1 • Spring 2005
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