Adjoints of ideals in regular local rings
| dc.creator | Lipman, Joseph | |
| dc.date | 1994-05-20 | |
| dc.date.accessioned | 2026-07-07T09:06:05Z | |
| dc.date.available | 2026-07-07T09:06:05Z | |
| dc.description | The adjoint of an ideal I in a regular local ring R is the R-ideal adj(I):=H^0(Y, Iω_Y), where f:Y -> Spec(R) is a proper birational map with Y nonsingular and IO_Y invertible, and ω_f is a canonical relative dualizing sheaf. (Such an f is supposed to exist.) The basic conjecture is that I.adj(I^n)=adj(I^{n+1}) whenever n is >= the analytic spread of I. This is a strong version of the Briancon-Skoda theorem, implying all other known versions. It follows from the (conjectural) vanishing of H^i(Y,ω_Y) for all i>0. When R is essentially of finite type over a char. 0 field, that vanishing has been deduced by Cutkosky from Kodaira vanishing. It also holds whenever dim.R = 2; and in this case we can say considerably more about adjoints, tying in e.g., with classical material on adjoint curves and conductors. | |
| dc.description | 12 pages, Amstex 2.1 | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9405010 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9405010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149895 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.title | Adjoints of ideals in regular local rings | |
| dc.type | text |