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arXiv · 1911.05290

Local deformations of branched projective structures: Schiffer variations and the Teichm\"uller map

Stefano Francaviglia·Lorenzo Ruffoni
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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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Stefano Francaviglia, Lorenzo Ruffoni. 2019-11-13. Local deformations of branched projective structures: Schiffer variations and the Teichm\"uller map. https://doi.org/10.1007/s10711-021-00601-6

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