Socle degrees for local cohomology modules of thickenings of maximal minors and sub-maximal Pfaffians

2022/12/13 by Li, Jiamin, Perlman, Michael
#13D45 #14F10 #14M12 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.06899

Abstract

Let S be the polynomial ring on the space of non-square generic matrices or the space of odd-sized skew-symmetric matrices, and let I be the determinantal ideal of maximal minors or Pf the ideal of sub-maximal Pfaffians, respectively. Using desingularizations and representation theory of the general linear group we expand upon work of Raicu--Weyman--Witt to determine the S-module structures of Ext^j_S(S/I^t, S) and Ext^j_S(S/Pf^t, S), from which we get the degrees of generators of these Ext modules. As a consequence, via graded local duality we answer a question of Wenliang Zhang on the socle degrees of local cohomology modules of the form H^j_\mathfrakm(S/I^t).

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