dc.contributor.author Biswas, I. dc.contributor.author Dan, A. dc.contributor.author Paul, A. dc.contributor.author Saha, A. dc.date.accessioned 2017-05-03T05:20:53Z dc.date.available 2017-05-03T05:20:53Z dc.date.issued 2017 dc.identifier.uri http://hdl.handle.net/20.500.11824/670 dc.description.abstract Let $E_G$ be a holomorphic principal $G$--bundle on a compact connected Riemann surface $X$, where $G$ is a connected reductive complex affine algebraic group. Fix a finite subset $D\, \subset\, X$, and for each $x\,\in\, D$ fix $w_x\, \in\, en_US \text{ad}(E_G)_x$. Let $T$ be a maximal torus in the group of all holomorphic automorphisms of $E_G$. We give a necessary and sufficient condition for the existence of a $T$--invariant logarithmic connection on $E_G$ singular over $D$ such that the residue over each $x\, \in\, D$ is $w_x$. We also give a necessary and sufficient condition for the existence of a logarithmic connection on $E_G$ singular over $D$ such that the residue over each $x\, \in\, D$ is $w_x$, under the assumption that each $w_x$ is $T$--rigid. dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Logarithmic connection en_US dc.subject residue en_US dc.subject automorphism en_US dc.subject maximal tori en_US dc.title Logarithmic connections on principal bundles over a Riemann surface en_US dc.type info:eu-repo/semantics/doctoralThesis en_US dc.relation.publisherversion https://arxiv.org/abs/1705.00852 en_US dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/615655 en_US dc.relation.projectID ES/1PE/SEV-2013-0323 en_US dc.rights.accessRights info:eu-repo/semantics/embargoedAccess en_US dc.type.hasVersion info:eu-repo/semantics/submittedVersion en_US dc.journal.title arxiv en_US
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