Powers of complete intersections: graded Betti numbers and applications
| dc.creator | Guardo, Elena | |
| dc.creator | Van Tuyl, Adam | |
| dc.date | 2004-09-06 | |
| dc.date | 2005-03-21 | |
| dc.date.accessioned | 2026-07-07T05:11:51Z | |
| dc.date.available | 2026-07-07T05:11:51Z | |
| dc.description | 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. | |
| dc.description | 15 pages, minor corrections, to appear in Ill. J. Math | |
| dc.identifier | https://arxiv.org/abs/math/0409090 | |
| dc.identifier | http://arxiv.org/abs/math/0409090 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72382 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13D40; 13D02; 13H10; 14A15 | |
| dc.title | Powers of complete intersections: graded Betti numbers and applications | |
| dc.type | text |