Local deformations of branched projective structures: Schiffer variations and the Teichmüller map

Stefano Francaviglia; Lorenzo Ruffoni

doi:10.1007/s10711-021-00601-6

Local deformations of branched projective structures: Schiffer variations and the Teichmüller map

Stefano Francaviglia
, Lorenzo Ruffoni

Mathematics and Statistics

Binghamton University

University of Bologna

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English
Pages (from-to)	21-48
Number of pages	28
Journal	Geometriae Dedicata
Volume	214
Issue number	1
DOIs	https://doi.org/10.1007/s10711-021-00601-6
State	Published - Oct 2021

Keywords

Beltrami differentials
Complex projective structures
Holonomy
Hyperelliptic curves
Movements of branch points

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10.1007/s10711-021-00601-6

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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.",

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author = "Stefano Francaviglia and Lorenzo Ruffoni",

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AU - Ruffoni, Lorenzo

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N2 - 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.

AB - 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.

KW - Beltrami differentials

KW - Complex projective structures

KW - Holonomy

KW - Hyperelliptic curves

KW - Movements of branch points

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DO - 10.1007/s10711-021-00601-6

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JO - Geometriae Dedicata

JF - Geometriae Dedicata

IS - 1

ER -

Local deformations of branched projective structures: Schiffer variations and the Teichmüller map

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Keywords

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