Regularity jumps for powers of ideals
| dc.creator | Conca, Aldo | |
| dc.date | 2003-10-31 | |
| dc.date.accessioned | 2026-07-07T05:02:25Z | |
| dc.date.available | 2026-07-07T05:02:25Z | |
| dc.description | The Castelnuovo-Mumford regularity $\reg(I)$ is one of the most important invariants of a homogeneous ideal $I$ in a polynomial ring. A basic question is how the regularity behaves with respect to taking powers of ideals. It is known that in the long-run $\reg(I^k)$ is a linear function of $k$. We show that in the short-run the regularity of $I^k$ can be quite "irregular". For any given integer $d>1$ we construct an ideal $J$ generated by $d+5$ monomials of degree $d+1$ in 4 variables such that $\reg(J^k)=k(d+1)$ for every $k<d$ and $\reg(J^d)\geq d(d+1)+d-1$. | |
| dc.identifier | https://arxiv.org/abs/math/0310493 | |
| dc.identifier | http://arxiv.org/abs/math/0310493 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69042 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13D02, 13P10 | |
| dc.title | Regularity jumps for powers of ideals | |
| dc.type | text |