2005/11/02 by Sébastien Jansou, Jansou, Sebastien
Mathematics · #14L30 #20G05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.math/0511046
openalex publication_date 2005/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).