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Euler obstruction and Lipschitz–Killing curvatures

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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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  1. Institut de Mathématiques de Marseille, Aix-Marseille Université CNRS, Centrale Marseille, I2M, UMR 7373, 13453, Marseille, Cedex 13, France

    Nicolas Dutertre

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Correspondence to Nicolas Dutertre.

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Dutertre, N. Euler obstruction and Lipschitz–Killing curvatures. Isr. J. Math. 213, 109–137 (2016). https://doi.org/10.1007/s11856-016-1322-9

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  • DOI: https://doi.org/10.1007/s11856-016-1322-9

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