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.

Francaviglia S., Ruffoni L. (2021). Local deformations of branched projective structures: Schiffer variations and the Teichmüller map. GEOMETRIAE DEDICATA, 214(1), 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.
2021
Francaviglia S., Ruffoni L. (2021). Local deformations of branched projective structures: Schiffer variations and the Teichmüller map. GEOMETRIAE DEDICATA, 214(1), 21-48 [10.1007/s10711-021-00601-6].
Francaviglia S.; Ruffoni L.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/835432
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