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Statements

Subject Item
dbr:Narasimhan–Seshadri_theorem
rdf:type
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rdfs:label
Narasimhan–Seshadri theorem
rdfs:comment
In mathematics, the Narasimhan–Seshadri theorem, proved by Narasimhan and Seshadri, says that a holomorphic vector bundle over a Riemann surface is stable if and only if it comes from an irreducible projective unitary representation of the fundamental group.
dcterms:subject
dbc:Riemann_surfaces dbc:Theorems_in_analysis
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35098864
dbo:wikiPageRevisionID
1053254517
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dbr:Differential_geometry dbr:Vector_bundle dbr:Fundamental_group dbr:Simple_module dbr:Scalar_curvature dbr:Kobayashi–Hitchin_correspondence dbr:Monodromy dbr:Curvature dbr:Nonabelian_Hodge_correspondence dbr:Stable_vector_bundle dbr:Mathematics dbr:Unitary_representation dbr:Stable_bundle dbc:Theorems_in_analysis dbr:Holomorphic_function dbc:Riemann_surfaces dbr:Riemann_surface dbr:Annals_of_Mathematics
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dbt:Citation dbt:Harvs
dbp:last
Narasimhan Seshadri
dbp:year
1965
dbo:abstract
In mathematics, the Narasimhan–Seshadri theorem, proved by Narasimhan and Seshadri, says that a holomorphic vector bundle over a Riemann surface is stable if and only if it comes from an irreducible projective unitary representation of the fundamental group. The main case to understand is that of topologically trivial bundles, i.e. those of degree zero (and the other cases are a minor technical extension of this case). This case of the Narasimhan–Seshadri theorem says that a degree zero holomorphic vector bundle over a Riemann surface is stable if and only if it comes from an irreducible unitary representation of the fundamental group of the Riemann surface. Donaldson gave another proof using differential geometry, and showed that the stable vector bundles have an essentially unique unitary connection of constant (scalar) curvature. In the degree zero case, Donaldson's version of the theorem says that a degree zero holomorphic vector bundle over a Riemann surface is stable if and only if it admits a flat unitary connection compatible with its holomorphic structure. Then the fundamental group representation appearing in the original statement is just the monodromy representation of this flat unitary connection.
dbp:author1Link
M. S. Narasimhan
dbp:author2Link
C. S. Seshadri
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wikipedia-en:Narasimhan–Seshadri_theorem?oldid=1053254517&ns=0
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2340
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wikipedia-en:Narasimhan–Seshadri_theorem