dc.contributor.author Biswas I. en_US dc.contributor.author Dan A. en_US dc.contributor.author Paul A. en_US dc.date.accessioned 2017-04-24T10:55:47Z dc.date.available 2017-04-24T10:55:47Z dc.date.issued 2017-04-01 dc.identifier.issn 0025-2611 dc.identifier.uri http://hdl.handle.net/20.500.11824/667 dc.description.abstract A theorem of Weil and Atiyah says that a holomorphic vector bundle $E$ on a compact Riemann surface $X$ admits a holomorphic connection if and only if the degree of every direct summand of $E$ is zero. Fix a finite subset $S$ of $X$, and fix an endomorphism $A(x)\, \in\, \text{End}(E_x)$ for every $x\, \in\, S$. It is natural to ask when there is a logarithmic connection on $E$ singular over $S$ with residue $A(x)$ at every $x\, \in\, S$. We give a necessary and sufficient condition for it under the assumption that the residues $A(x)$ are rigid. en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.publisher Manucripta Mathematica en_US dc.relation info:eu-repo/grantAgreement/EC/FP7/615655 en_US dc.relation ES/1PE/SEV-2013-0323 en_US dc.rights info:eu-repo/semantics/openAccess 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 rigidity en_US dc.subject logarithmic Atiyah bundle en_US dc.title Criterion for logarithmic connections with prescribed residues en_US dc.type info:eu-repo/semantics/article en_US dc.type info:eu-repo/semantics/publishedVersion en_US dc.identifier.doi 10.1007/s00229-017-0935-6 dc.relation.publisherversion http://link.springer.com/article/10.1007/s00229-017-0935-6 en_US
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