The invariant Quot scheme

[摘要] Given an affine scheme X with an action of a reductive group G and a G-linearized coherent sheaf M, we construct the invariant Quot scheme that parametrizes the quotients of,M whose space of global sections is a direct sum of simple G-modules with fixed finite multiplicities. Then we determine the invariant Quot scheme in a simple situation, where X is the cone of primitive vectors of a simple G-module and M is the free sheaf on X generated by another simple G-module. This invariant Quot scheme has only one point, that is reduced in most of the cases. The only cases where it is not reduced occur when X is the cone of primitive vectors of a quadratic vector space V of odd dimension, under the action of Spin(V). (c) 2006 Elsevier Inc. Tous droits reserves.

[发布日期] 2006-12-15