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Index theorems for holomorphic maps and foliations

Marco Abate·Filippo Bracci·Francesca Tovena
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Abstract

We describe a general construction providing index theorems localizing the Chern classes of the normal bundle of a subvariety inside a complex manifold. As particular instances of our construction we recover both Lehmann-Suwa's generalization of the classical Camacho-Sad index theorem for holomorphic foliations and our index theorem for holomorphic maps with positive dimensional fixed point set. Furthermore, we also obtain generalizations of recent index theorems of Camacho-Movasati-Sad and Camacho-Lehmann for holomorphic foliations transversal to a subvariety.

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Marco Abate, Filippo Bracci, Francesca Tovena. 2006-01-25. Index theorems for holomorphic maps and foliations. https://arxiv.org/abs/math/0601602

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