Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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S. Francaviglia - L. Ruffoni

Local deformations of branched projective structures: Schiffer variations and the Teichm├╝ller map

created by ruffoni on 21 Dec 2019
modified on 01 Jun 2022

[BibTeX]

Published Paper

Inserted: 21 dec 2019
Last Updated: 1 jun 2022

Journal: Geometriae Dedicata
Year: 2021
Doi: https://doi.org/10.1007/s10711-021-00601-6

ArXiv: 1911.05290 PDF
Links: Journal

Abstract:

We study a class of continuous deformations of branched complex projective structures on closed surfaces of genus $g\geq 2$, which preserve the holonomy representation of the structure and the order of the branch points. In the case of non-elementary holonomy we show that when the underlying complex structure is infinitesimally preserved the branch points are necessarily arranged on a canonical divisor, and we establish a partial converse for hyperelliptic structures.

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