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Index theorems for holomorphic maps and foliations

Research paper by Marco Abate, Filippo Bracci, Francesca Tovena

Indexed on: 25 Jan '06Published on: 25 Jan '06Published in: Mathematics - Complex Variables



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.