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June 2019 Note on MacPherson’s Local Euler Obstruction
Yunfeng Jiang
Michigan Math. J. 68(2): 227-250 (June 2019). DOI: 10.1307/mmj/1548817530

Abstract

This is a note on MacPherson’s local Euler obstruction, which plays an important role recently in the Donaldson–Thomas theory by the work of Behrend.

We introduce MacPherson’s original definition and prove that it is equivalent to the algebraic definition used by Behrend, following the method of González-Sprinberg. We also give a formula of the local Euler obstruction in terms of Lagrangian intersections. As an application, we consider a scheme or DM stack X admitting a symmetric obstruction theory. Furthermore, we assume that there is a C action on X that makes the obstruction theory C-equivariant. The C-action on the obstruction theory naturally gives rise to a cosection map in the Kiem–Li sense. We prove that Behrend’s weighted Euler characteristic of X is the same as the Kiem–Li localized invariant of X by the C-action.

Citation

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Yunfeng Jiang. "Note on MacPherson’s Local Euler Obstruction." Michigan Math. J. 68 (2) 227 - 250, June 2019. https://doi.org/10.1307/mmj/1548817530

Information

Received: 11 April 2017; Revised: 3 July 2017; Published: June 2019
First available in Project Euclid: 30 January 2019

zbMATH: 07084761
MathSciNet: MR3961215
Digital Object Identifier: 10.1307/mmj/1548817530

Subjects:
Primary: 14N35
Secondary: 14A20

Rights: Copyright © 2019 The University of Michigan

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Vol.68 • No. 2 • June 2019
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