2023/09/14 by András C. Lőrincz, Michael D. Perlman, Lőrincz, András C. +1
Mathematics · #11S90 #13A50 #13D45 #14B15 #14F10 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2309.07697
openalex publication_date 2023/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study D-modules and related invariants on the space of 2 x 2 x n hypermatrices for n >= 3, which has finitely many orbits under the action of G = GL2 x GL2 x GLn. We describe the category of coherent G-equivariant D-modules as the category of representations of a quiver with relations. We classify the simple equivariant D-modules, determine their characteristic cycles and find special representations that appear in their G-structures. We determine the explicit D-module structure of the local cohomology groups with supports given by orbit closures. As a consequence, we calculate the Lyubeznik numbers and intersection cohomology groups of the orbit closures. All but one of the orbit closures have rational singularities: we use local cohomology to prove that the one exception is neither normal nor Cohen--Macaulay. While our results display special behavior in the cases n=3 and n=4, they are completely uniform for n >= 5.