About: Narasimhan–Seshadri theorem

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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.

Attributes	Values
rdf:type	yago:Artifact100021939 yago:Object100002684 yago:PhysicalEntity100001930 yago:Surface104362025 yago:Whole100003553 yago:WikicatRiemannSurfaces
rdfs:label	Narasimhan–Seshadri theorem (en)
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. (en)
dcterms:subject	Riemann surfaces Theorems in analysis
Wikipage page ID	35098864 (xsd:integer)
Wikipage revision ID	1053254517 (xsd:integer)
Link from a Wikipage to another Wikipage	Scalar curvature Annals of Mathematics Holomorphic function Riemann surface Riemann surfaces Mathematics Monodromy Stable vector bundle Fundamental group Curvature Kobayashi–Hitchin correspondence Theorems in analysis Differential geometry Unitary representation Vector bundle Nonabelian Hodge correspondence Simple module Stable bundle
Link from a Wikipage to an external page	https://projecteuclid.org/euclid.jdg/1214437664
sameAs	Narasimhan–Seshadri theorem Narasimhan–Seshadri theorem Narasimhan–Seshadri theorem
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harvs
last	Narasimhan (en) Seshadri (en)
year	1965 (xsd:integer)
has 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. (en)
author1-link	M. S. Narasimhan (en)
author2-link	C. S. Seshadri (en)
prov:wasDerivedFrom	wikipedia-en:Narasimhan–Seshadri_theorem?oldid=1053254517&ns=0
page length (characters) of wiki page	2340 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Narasimhan–Seshadri_theorem
is Link from a Wikipage to another Wikipage of	List of Shanti Swarup Bhatnagar Prize recipients Deaths in May 2021 Gauge theory (mathematics) Quillen metric Christopher Deninger Loyola College, Chennai Loyola College, Chennai M. S. Narasimhan Stable vector bundle C. S. Seshadri K-stability List of Brahmins Kobayashi–Hitchin correspondence Narasimhan-Seshadri theorem Yang–Mills equations Nonabelian Hodge correspondence Projective flatness Moduli space of representations
is Wikipage redirect of	Narasimhan-Seshadri theorem Projective flatness Moduli space of representations
is known for of	C. S. Seshadri
is known for of	C. S. Seshadri
is foaf:primaryTopic of	wikipedia-en:Narasimhan–Seshadri_theorem

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