Siegel domain
E871401
A Siegel domain is a type of complex analytic domain used in several complex variables and automorphic forms, generalizing upper half-planes to higher dimensions.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Siegel domain canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10543865 — 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: Siegel domain Context triple: [Carl Ludwig Siegel, notableWork, Siegel domain]
-
A.
Poincaré upper half-plane model
The Poincaré upper half-plane model is a standard representation of the hyperbolic plane using the complex numbers with positive imaginary part, equipped with a specific metric that makes geodesics appear as semicircles and vertical lines.
-
B.
Fuchsian group
A Fuchsian group is a discrete group of isometries of the hyperbolic plane, fundamental in the study of Riemann surfaces, modular forms, and hyperbolic geometry.
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C.
Klein quartic
The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
-
D.
Kleinian group
A Kleinian group is a discrete subgroup of Möbius transformations acting on hyperbolic 3-space, central to the study of Riemann surfaces, complex dynamics, and low-dimensional topology.
-
E.
Blaschke
Blaschke is a German surname most notably associated with Wilhelm Blaschke, a prominent mathematician known for his contributions to differential and convex 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: Siegel domain Target entity description: A Siegel domain is a type of complex analytic domain used in several complex variables and automorphic forms, generalizing upper half-planes to higher dimensions.
-
A.
Poincaré upper half-plane model
The Poincaré upper half-plane model is a standard representation of the hyperbolic plane using the complex numbers with positive imaginary part, equipped with a specific metric that makes geodesics appear as semicircles and vertical lines.
-
B.
Fuchsian group
A Fuchsian group is a discrete group of isometries of the hyperbolic plane, fundamental in the study of Riemann surfaces, modular forms, and hyperbolic geometry.
-
C.
Klein quartic
The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
-
D.
Kleinian group
A Kleinian group is a discrete subgroup of Möbius transformations acting on hyperbolic 3-space, central to the study of Riemann surfaces, complex dynamics, and low-dimensional topology.
-
E.
Blaschke
Blaschke is a German surname most notably associated with Wilhelm Blaschke, a prominent mathematician known for his contributions to differential and convex geometry.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
complex analytic domain
ⓘ
domain in several complex variables ⓘ generalization of upper half-plane ⓘ |
| appearsIn |
Langlands program
NERFINISHED
ⓘ
theory of Eisenstein series ⓘ theory of automorphic representations ⓘ theory of theta functions ⓘ |
| definedOver | complex numbers ⓘ |
| definedUsing |
Hermitian form
ⓘ
imaginary part conditions ⓘ open convex cone ⓘ |
| generalizes |
Siegel upper half-space
NERFINISHED
ⓘ
upper half-plane ⓘ |
| hasApplication |
Hodge theory
ⓘ
construction of automorphic forms ⓘ lattice counting problems ⓘ study of abelian varieties ⓘ study of moduli spaces ⓘ |
| hasCoordinateDescription | given by inequalities involving an imaginary part and a cone ⓘ |
| hasDimension | higher-dimensional complex manifold ⓘ |
| hasHistoricalDevelopment | introduced in the 20th century ⓘ |
| hasMainUse | realization of arithmetic quotients as complex manifolds ⓘ |
| hasProperty |
holomorphically convex (in typical constructions)
ⓘ
pseudoconvex (in standard settings) ⓘ |
| hasStructure | complex manifold ⓘ |
| hasType |
Siegel domain of the first kind
NERFINISHED
ⓘ
Siegel domain of the second kind ⓘ |
| namedAfter | Carl Ludwig Siegel NERFINISHED ⓘ |
| relatedConcept |
Harish-Chandra realization
NERFINISHED
ⓘ
Jordan algebra ⓘ Siegel modular variety NERFINISHED ⓘ symplectic group Sp(2g, R) NERFINISHED ⓘ tube domain ⓘ |
| relatedTo |
Hermitian symmetric space
ⓘ
bounded symmetric domain ⓘ symmetric space of non-compact type ⓘ |
| specialCase |
Siegel upper half-space of degree g
NERFINISHED
ⓘ
upper half-plane ⓘ |
| studiedIn |
analytic number theory
ⓘ
complex analysis ⓘ differential geometry ⓘ |
| usedIn |
algebraic geometry
ⓘ
arithmetic geometry ⓘ automorphic forms ⓘ representation theory ⓘ several complex variables ⓘ theory of modular forms ⓘ |
| usedToModel |
Hermitian symmetric spaces of tube type
ⓘ
certain bounded symmetric domains ⓘ |
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: Siegel domain Description of subject: A Siegel domain is a type of complex analytic domain used in several complex variables and automorphic forms, generalizing upper half-planes to higher dimensions.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.