Mathematics – Commutative Algebra
Scientific paper
1994-05-20
Mathematics
Commutative Algebra
12 pages, Amstex 2.1
Scientific paper
The adjoint of an ideal I in a regular local ring R is the R-ideal adj(I):=H^0(Y, I\omega_Y), where f:Y -> Spec(R) is a proper birational map with Y nonsingular and IO_Y invertible, and \omega_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,\omega_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.
No associations
LandOfFree
Adjoints of ideals in regular local rings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Adjoints of ideals in regular local rings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Adjoints of ideals in regular local rings will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-575977