Index theorems for couples of holomorphic self-maps

Paolo Arcangeli

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arXiv · 1604.01569

Index theorems for couples of holomorphic self-maps

Paolo Arcangeli

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Abstract

Let $M$ be a $n$-dimensional complex manifold and $f,g:M\to M$ two distinct holomorphic self-maps. Suppose that $f$ and $g$ coincide on a globally irreducible compact hypersurface $S\subset M$. We show that if one of the two maps is a local biholomorphism around $S'=S-\text{Sing}(S)$ and, if needed, $S'$ sits into $M$ in a particular nice way, then it is possible to define a $1$-dimensional holomorphic (possibly singular) foliation on $S'$ and partial holomorphic connections on certain holomorphic vector bundles on $S'$. As a consequence, we are able to localize suitable characteristic classes and thus to get index theorems.

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BibTeX RIS

Paolo Arcangeli. 2016-04-06. Index theorems for couples of holomorphic self-maps. https://arxiv.org/abs/1604.01569

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