Euler obstruction and Lipschitz-Killing curvatures

2014/05/23 by Nicolas Dutertre, Dutertre, Nicolas
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.AG #math.DG

paper · pdf · doi:10.48550/arxiv.1405.6152

arxiv created 2014/05/23 · arxiv updated 2014/05/26

Abstract

Applying a local Gauss-Bonnet formula for closed subanalytic sets to the complex analytic case, we obtain characterizations of the Euler obstruction of a complex analytic germ in terms of the Lipschitz-Killing curvatures and the Chern forms of its regular part. We also prove analogous results for the global Euler obstruction. As a corollary, we give a positive answer to a question of Fu on the Euler obstruction and the Gauss-Bonnet measure.

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