D-module structure of local cohomology modules of toric algebras

摘要

Let S be a toric algebra over a field K of characteristic 0 and let I be amonomial ideal of S. We show that the local cohomology modules H^i_I(S) are offinite length over the ring of differential operators D(S;K), generalizing theclassical case of a polynomial algebra S. As an application, we compute thecharacteristic cycles of some local cohomology modules.