We study a class of continuous deformations of branched complex projective structures on closed surfaces of genus g≥ 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.
Local deformations of branched projective structures: Schiffer variations and the Teichmüller map / Francaviglia S.; Ruffoni L.. - In: GEOMETRIAE DEDICATA. - ISSN 0046-5755. - STAMPA. - 214:1(2021), pp. 21-48. [10.1007/s10711-021-00601-6]
Local deformations of branched projective structures: Schiffer variations and the Teichmüller map
Francaviglia S.;
2021
Abstract
We study a class of continuous deformations of branched complex projective structures on closed surfaces of genus g≥ 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.| File | Dimensione | Formato | |
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