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In mathematics, specifically in symplectic topology and algebraic geometry, one can construct the moduli space of stable maps, satisfying specified conditions, from Riemann surfaces into a given symplectic manifold. This moduli space is the essence of the Gromov–Witten invariants, which find application in enumerative geometry and type IIA string theory. The idea of stable map was proposed by Maxim Kontsevich around 1992 and published in . Because the construction is lengthy and difficult, it is carried out here rather than in the Gromov–Witten invariants article itself.

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rdf:type	yago:WikicatComplexManifolds yago:Artifact100021939 yago:Conduit103089014 yago:Manifold103717750 yago:Object100002684 yago:Passage103895293 yago:PhysicalEntity100001930 yago:Pipe103944672 yago:YagoGeoEntity yago:YagoPermanentlyLocatedEntity yago:Tube104493505 yago:Way104564698 yago:Whole100003553
rdfs:label	Stabile Abbildung (de) 安定写像 (ja) Stable map (en)
rdfs:comment	In der symplektischen Topologie kann man den Modulraum stabiler Abbildungen, von Riemannschen Flächen in eine gegebene symplektische Mannigfaltigkeit definieren. Dieser Modulraum ist wesentlich für die Konstruktion der Gromov-Witten-Invarianten, die in der abzählenden algebraischen Geometrie und der Stringtheorie Anwendung finden. (de) In mathematics, specifically in symplectic topology and algebraic geometry, one can construct the moduli space of stable maps, satisfying specified conditions, from Riemann surfaces into a given symplectic manifold. This moduli space is the essence of the Gromov–Witten invariants, which find application in enumerative geometry and type IIA string theory. The idea of stable map was proposed by Maxim Kontsevich around 1992 and published in . Because the construction is lengthy and difficult, it is carried out here rather than in the Gromov–Witten invariants article itself. (en) 数学、特にシンプレクティックトポロジーや代数幾何学では、リーマン面から与えられるシンプレクティック多様体への特別な条件を満たす安定写像(stable maps)のモジュライ空間を構成することができる。このモジュライ空間が、グロモフ・ウィッテン不変量の本質的であり、数え上げ幾何学やなどの弦理論への応用がある。安定写像の考え方は、マキシム・コンツェビッチ(Maxim Kontsevich)により、1992年頃に提案され、で出版された。安定写像を構成することは長く難しいので、グロモフ・ウィッテン不変量の記事の中ではなく、むしろ本記事で展開する。 (ja)
dcterms:subject	Moduli theory Complex manifolds String theory Symplectic topology
Wikipage page ID	2300947 (xsd:integer)
Wikipage revision ID	1009847112 (xsd:integer)
Link from a Wikipage to another Wikipage	Enumerative geometry Moduli theory Almost complex manifold Complex manifolds Atiyah-Singer index theorem Riemann surface Pseudoholomorphic curve String theory Compact space Mathematics Maxim Kontsevich Elliptic operator Branched covering Sard's theorem Symplectic topology Lp space Sobolev space Closed manifold Symplectic manifold Cauchy–Riemann equations Algebraic geometry Banach manifold Fano variety Homology (mathematics) Moduli space Fredholm operator Gromov–Witten invariant Implicit function theorem Natural number Orbifold Rational number Euler characteristic Elliptic regularity Symplectic form Symplectic topology Deligne–Mumford moduli space of curves Type IIA string theory dbr:Pseudocycle
sameAs	Stable map Stable map Stable map Stable map Stable map Stable map
dbp:wikiPageUsesTemplate	dbt:Cite_journal dbt:Harvtxt dbt:Technical dbt:Isbn
has abstract	In der symplektischen Topologie kann man den Modulraum stabiler Abbildungen, von Riemannschen Flächen in eine gegebene symplektische Mannigfaltigkeit definieren. Dieser Modulraum ist wesentlich für die Konstruktion der Gromov-Witten-Invarianten, die in der abzählenden algebraischen Geometrie und der Stringtheorie Anwendung finden. (de) In mathematics, specifically in symplectic topology and algebraic geometry, one can construct the moduli space of stable maps, satisfying specified conditions, from Riemann surfaces into a given symplectic manifold. This moduli space is the essence of the Gromov–Witten invariants, which find application in enumerative geometry and type IIA string theory. The idea of stable map was proposed by Maxim Kontsevich around 1992 and published in . Because the construction is lengthy and difficult, it is carried out here rather than in the Gromov–Witten invariants article itself. (en) 数学、特にシンプレクティックトポロジーや代数幾何学では、リーマン面から与えられるシンプレクティック多様体への特別な条件を満たす安定写像(stable maps)のモジュライ空間を構成することができる。このモジュライ空間が、グロモフ・ウィッテン不変量の本質的であり、数え上げ幾何学やなどの弦理論への応用がある。安定写像の考え方は、マキシム・コンツェビッチ(Maxim Kontsevich)により、1992年頃に提案され、で出版された。安定写像を構成することは長く難しいので、グロモフ・ウィッテン不変量の記事の中ではなく、むしろ本記事で展開する。 (ja)
prov:wasDerivedFrom	wikipedia-en:Stable_map?oldid=1009847112&ns=0
page length (characters) of wiki page	8678 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Stable_map
is rdfs:seeAlso of	Stable curve
is Link from a Wikipage to another Wikipage of	Behrend function David Mumford Index of physics articles (S) Pseudoholomorphic curve Maxim Kontsevich Gromov–Witten invariant Stable curve Space of stable maps
is Wikipage redirect of	Space of stable maps
is foaf:primaryTopic of	wikipedia-en:Stable_map

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