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- W1523544562 abstract "This is a note on MacPherson's local Euler obstruction, which plays an important role recently in 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 Gonzalez-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 $CC^*$ action on $X$, which makes the obstruction theory $CC^*$-equivariant. The $CC^*$-action on the obstruction theory naturally gives rise to a cosection map in the sense of Kiem-Li. We prove that Behrend's weighted Euler characteristic of $X$ is the same as Kiem-Li localized invariant of $X$ by the $CC^*$-action." @default.
- W1523544562 created "2016-06-24" @default.
- W1523544562 creator A5088366355 @default.
- W1523544562 date "2014-12-11" @default.
- W1523544562 modified "2023-10-14" @default.
- W1523544562 title "Note on MacPherson's local Euler obstruction" @default.
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- W1523544562 doi "https://doi.org/10.48550/arxiv.1412.3720" @default.
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