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Branched projective structures, branched SO(3,C)-opers and logarithmic connections on jet bundle | | Indranil Biswas
; Sorin Dumitrescu
; | | Date: |
21 Jul 2020 | | Abstract: | We study the branched holomorphic projective structures on a compact Riemann
surface $X$ with a fixed branching divisor $S, =, sum_{i=1}^d x_i$, where
$x_i ,in, X$ are distinct points. After defining branched ${
m
SO}(3,{mathbb C})$--opers, we show that the branched holomorphic projective
structures on $X$ are in a natural bijection with the branched ${
m
SO}(3,{mathbb C})$--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 $J^2((TX)otimes {mathcal
O}_X(S))$ singular over $S$, satisfying certain natural geometric conditions. | | Source: | arXiv, 2007.10651 | | Services: | Forum | Review | PDF | Favorites | |
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