“The self-duality equations on a Riemann surface”
E886936
“The self-duality equations on a Riemann surface” is a seminal mathematical paper that introduced what are now called Hitchin equations, laying foundational connections between gauge theory, Higgs bundles, and the geometry of moduli spaces on Riemann surfaces.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Hitchin equations | 2 |
| Stable bundles and integrable systems (Hitchin, 1987) | 1 |
| “The self-duality equations on a Riemann surface” canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10829573 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: “The self-duality equations on a Riemann surface” Context triple: [Nigel Hitchin, notableWork, “The self-duality equations on a Riemann surface”]
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A.
Seiberg–Witten invariants
Seiberg–Witten invariants are powerful topological invariants of smooth four-manifolds derived from solutions to the Seiberg–Witten equations, used to distinguish different smooth structures and study the geometry and topology of 4D spaces.
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B.
Seiberg–Witten differential
The Seiberg–Witten differential is a meromorphic one-form on the Seiberg–Witten curve whose periods encode the low-energy effective couplings and BPS spectrum of certain supersymmetric gauge theories.
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C.
Differential Analysis on Complex Manifolds
"Differential Analysis on Complex Manifolds" is a foundational mathematical monograph that systematically develops the theory of differential and complex geometry on complex manifolds.
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D.
Einstein–Yang–Mills equations
The Einstein–Yang–Mills equations are the coupled field equations that describe how non-abelian gauge fields (such as those in Yang–Mills theory) interact with and curve spacetime within the framework of general relativity.
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E.
Atiyah–Singer index theorem
The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: “The self-duality equations on a Riemann surface” Target entity description: “The self-duality equations on a Riemann surface” is a seminal mathematical paper that introduced what are now called Hitchin equations, laying foundational connections between gauge theory, Higgs bundles, and the geometry of moduli spaces on Riemann surfaces.
-
A.
Seiberg–Witten invariants
Seiberg–Witten invariants are powerful topological invariants of smooth four-manifolds derived from solutions to the Seiberg–Witten equations, used to distinguish different smooth structures and study the geometry and topology of 4D spaces.
-
B.
Seiberg–Witten differential
The Seiberg–Witten differential is a meromorphic one-form on the Seiberg–Witten curve whose periods encode the low-energy effective couplings and BPS spectrum of certain supersymmetric gauge theories.
-
C.
Differential Analysis on Complex Manifolds
"Differential Analysis on Complex Manifolds" is a foundational mathematical monograph that systematically develops the theory of differential and complex geometry on complex manifolds.
-
D.
Einstein–Yang–Mills equations
The Einstein–Yang–Mills equations are the coupled field equations that describe how non-abelian gauge fields (such as those in Yang–Mills theory) interact with and curve spacetime within the framework of general relativity.
-
E.
Atiyah–Singer index theorem
The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
journal article
ⓘ
mathematical research paper ⓘ |
| associatedConcept |
Hitchin base
ⓘ
Hitchin moduli space ⓘ
linked to:
Hitchin fibration
Hitchin section ⓘ Hitchin system ⓘ harmonic metric on a bundle ⓘ holomorphic structure on a vector bundle ⓘ polystable Higgs bundle ⓘ stable Higgs bundle ⓘ unitary connection ⓘ |
| author |
Nigel Hitchin
ⓘ
Nigel J. Hitchin ⓘ
linked to:
Nigel Hitchin
|
| defines | Hitchin equations ⓘ |
| field |
algebraic geometry
ⓘ
complex geometry ⓘ differential geometry ⓘ gauge theory ⓘ geometric analysis ⓘ mathematical physics ⓘ |
| hasInfluenceOn |
gauge-theoretic approaches to algebraic geometry
ⓘ
geometric Langlands program ⓘ hyperkähler geometry of moduli spaces ⓘ non-abelian Hodge theory ⓘ study of character varieties ⓘ theory of Higgs bundles ⓘ |
| introduces | Higgs bundle ⓘ |
| language | English ⓘ |
| mainTopic |
Higgs bundles
ⓘ
linked to:
Higgs bundle
Hitchin equations ⓘ Yang–Mills self-duality in two dimensions ⓘ moduli spaces of Higgs bundles ⓘ non-abelian Hodge theory ⓘ self-duality equations ⓘ stable bundles on Riemann surfaces ⓘ |
| publishedIn | Proceedings of the London Mathematical Society ⓘ |
| relatesTo |
Hitchin fibration
ⓘ
character varieties ⓘ flat connections ⓘ harmonic maps ⓘ integrable systems ⓘ moduli of stable bundles ⓘ non-abelian Hodge correspondence ⓘ
linked to:
non-abelian Hodge theory
representation varieties of surface groups ⓘ spectral curves ⓘ |
| studies |
holomorphic vector bundles with Higgs field
ⓘ
hyperkähler structure on moduli spaces ⓘ moduli space of solutions to Hitchin equations ⓘ solutions of self-duality equations on Riemann surfaces ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: “The self-duality equations on a Riemann surface” Description of subject: “The self-duality equations on a Riemann surface” is a seminal mathematical paper that introduced what are now called Hitchin equations, laying foundational connections between gauge theory, Higgs bundles, and the geometry of moduli spaces on Riemann surfaces.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: “The self-duality equations on a Riemann surface”
subject linked to:
“The self-duality equations on a Riemann surface”
linked to: “The self-duality equations on a Riemann surface”
subject linked to:
“The self-duality equations on a Riemann surface”
linked to: “The self-duality equations on a Riemann surface”