Branched projective structures on a riemann surface and logarithmic connections

Biswas, I and Dumitrescu, S and Gupta, S (2019) Branched projective structures on a riemann surface and logarithmic connections. In: Documenta Mathematica, 24 . pp. 2299-2337.

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Abstract

We study the branched holomorphic projective structures on a compact Riemann surface X with a fixed branching divisor S=∑i=1dxi, where xi∈X are distinct points. After defining branched SO (3 , C) -opers, we show that the branched holomorphic projective structures on X are in a natural bijection with the branched SO (3 , C) -opers singular at S. It is deduced that the branched holomorphic projective structures on X are also identified with a subset of the space of all logarithmic connections on J2((TX) ⊗ OX(S)) singular over S, satisfying certain natural geometric conditions.

Item Type:	Journal Article
Publication:	Documenta Mathematica
Publisher:	Deutsche Mathematiker Vereinigung
Additional Information:	The copyright for this article belongs to Deutsche Mathematiker Vereinigung.
Keywords:	Branched projective structure; Branched SO(3 , C) -oper; Differential operator; Logarithmic connection
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	02 Dec 2022 10:20
Last Modified:	02 Dec 2022 10:20
URI:	https://eprints.iisc.ac.in/id/eprint/78200

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