Powers of Ideals and Fibers of Morphisms
| dc.creator | Eisenbud, David | |
| dc.creator | Harris, Joe | |
| dc.date | 2008-07-26 | |
| dc.date.accessioned | 2026-07-07T09:53:10Z | |
| dc.date.available | 2026-07-07T09:53:10Z | |
| dc.description | Let X\subset PP^n be a projective scheme over a field, and let phi:X --> Y be a finite morphism. Our main result is a formula in terms of global data for the maximum of the Castelnuovo-Mumford regularity of the fibers of ϕ, considered as subschemes of \PP^n. From an algebraic point of view, our formula is related to the theorem of Cutkosky-Herzog-Trung and Kodiyalam showing that for any homogeneous ideal I in a standard graded algebra S, the regularity of I^t can be written as dt+εfor some non-negative integers d, ε, and all large t. In the special case where I contains a power of S_+ and is generated by forms of a single degree, our formula gives an interpretation of ε: it is one less than the maximum regularity of a fiber of the morphism associated to I. These formulas have strong consequences for ideals generated by generic forms. | |
| dc.identifier | https://arxiv.org/abs/0807.4243 | |
| dc.identifier | http://arxiv.org/abs/0807.4243 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165854 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14N05, 14B05, 14J40, 13D02 | |
| dc.title | Powers of Ideals and Fibers of Morphisms | |
| dc.type | text |