Local Euler obstructions for determinantal varieties

2021/05/01 by Lőrincz, András C., Raicu, Claudiu · 1 citation
#13A50 #14F10 #14F40 #14M12 #32S60 #55N33 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2105.00271

Abstract

The goal of this note is to explain a derivation of the formulas for the local Euler obstructions of determinantal varieties of general, symmetric and skew-symmetric matrices, by studying the invariant de Rham complex and using character formulas for simple equivariant D-modules. These calculations are then combined with standard arguments involving Kashiwara's local index formula and the description of characteristic cycles of simple equivariant D-modules. The formulas are implicit in the work of Boe and Fu, and in the case of general matrices they have also been obtained recently by Gaffney--Grulha--Ruas, for skew-symmetric matrices by Promtapan and Rimányi, and for all cases by Zhang.

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