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arXiv · 2105.00271

Local Euler obstructions for determinantal varieties

András C. Lőrincz·Claudiu Raicu
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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 Rim\'anyi, and for all cases by Zhang.

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András C. Lőrincz, Claudiu Raicu. 2021-05-01. Local Euler obstructions for determinantal varieties. https://arxiv.org/abs/2105.00271

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