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- W4367000287 abstract "A moduli space ${mathcal N}$ of stable parabolic vector bundles, of rank $r$ and parabolic degree zero, on a $n$-pointed curve has two naturally occurring holomorphic $T^*{mathcal N}$--torsors over it. One of them is given by the moduli space of pairs of the form $(E_*, D)$, where $E_* in {mathcal N}$ and $D$ is a connection on $E_*$. This $T^*{mathcal N}$--torsor has a $C^infty$ section that sends any $E_* in {mathcal N}$ to the unique connection on it with unitary monodromy. The other $T^*{mathcal N}$--torsor is given by the sheaf of holomorphic connections on a theta line bundle over ${mathcal N}$. This $T^*{mathcal N}$--torsor also has a $C^infty$ section given by the Hermitian structure on the theta bundle constructed by Quillen. We prove that these two $T^*{mathcal N}$--torsors are isomorphic by a canonical holomorphic map. This holomorphic isomorphism interchanges the above two $C^infty$ sections." @default.
- W4367000287 created "2023-04-27" @default.
- W4367000287 creator A5091389697 @default.
- W4367000287 date "2023-04-24" @default.
- W4367000287 modified "2023-10-01" @default.
- W4367000287 title "On some natural torsors over moduli spaces of parabolic bundles" @default.
- W4367000287 doi "https://doi.org/10.48550/arxiv.2304.12086" @default.
- W4367000287 hasPublicationYear "2023" @default.
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