Index theorems for holomorphic self-maps
| dc.creator | Abate, Marco | |
| dc.creator | Bracci, Filippo | |
| dc.creator | Tovena, Francesca | |
| dc.date | 2005-09-28 | |
| dc.date.accessioned | 2026-07-07T06:19:42Z | |
| dc.date.available | 2026-07-07T06:19:42Z | |
| dc.description | Let $M$ be a complex manifold and $S\subset M$ a (possibly singular) subvariety of $M$. Let $f\colon M\to M$ be a holomorphic map such that $f$ restricted to $S$ is the identity. We show that one can associate to $f$ a holomorphic section $X_f$ of a sheaf related to the embedding of $S$ in $M$ and that such a section reads the dynamical behavior of $f$ along $S$. In particular we prove that under generic hypotheses the canonical section $X_f$ induces a holomorphic action in the sense of Bott on the normal bundle of (the regular part of) $S$ in $M$ and this allows to obtain for holomorphic self-maps with non- isolated fixed points index theorems similar to Camacho-Sad, Baum-Bott and variation index theorems for holomorphic foliations. Finally we apply our index theorems to obtain information about topology and dynamics of holomorphic self-maps of surfaces with a compact curve of fixed points. | |
| dc.description | 46 pages, published version | |
| dc.identifier | https://arxiv.org/abs/math/0509669 | |
| dc.identifier | http://arxiv.org/abs/math/0509669 | |
| dc.identifier | Ann. of Math. (2), Vol. 159 (2004), no. 2, 819-864 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95116 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Complex Variables | |
| dc.title | Index theorems for holomorphic self-maps | |
| dc.type | text |