Differential Analysis on Complex Manifolds
E325283
"Differential Analysis on Complex Manifolds" is a foundational mathematical monograph that systematically develops the theory of differential and complex geometry on complex manifolds.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Differential Analysis on Complex Manifolds canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3072661 — 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: Differential Analysis on Complex Manifolds Context triple: [Annals of Mathematics Studies, hasNotableWork, Differential Analysis on Complex Manifolds]
-
A.
Singular Points of Complex Hypersurfaces
"Singular Points of Complex Hypersurfaces" is a foundational monograph in singularity theory that systematically studies the local and topological properties of singularities arising in complex algebraic and analytic hypersurfaces.
-
B.
Hodge theory
Hodge theory is a branch of mathematics that studies the relationship between differential forms, cohomology, and complex geometry, particularly on complex manifolds.
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C.
Riemann surfaces
Riemann surfaces are one-dimensional complex manifolds that provide the natural geometric setting for studying complex analytic functions and their multi-valued behavior.
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D.
Kähler manifold
A Kähler manifold is a complex manifold equipped with a Hermitian metric whose associated symplectic form is closed, making it simultaneously a complex, Riemannian, and symplectic manifold in a compatible way.
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E.
Deligne cohomology
Deligne cohomology is a refined cohomology theory in algebraic geometry that combines singular cohomology and differential forms to capture both topological and arithmetic information about complex algebraic varieties.
- 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: Differential Analysis on Complex Manifolds Target entity description: "Differential Analysis on Complex Manifolds" is a foundational mathematical monograph that systematically develops the theory of differential and complex geometry on complex manifolds.
-
A.
Singular Points of Complex Hypersurfaces
"Singular Points of Complex Hypersurfaces" is a foundational monograph in singularity theory that systematically studies the local and topological properties of singularities arising in complex algebraic and analytic hypersurfaces.
-
B.
Hodge theory
Hodge theory is a branch of mathematics that studies the relationship between differential forms, cohomology, and complex geometry, particularly on complex manifolds.
-
C.
Riemann surfaces
Riemann surfaces are one-dimensional complex manifolds that provide the natural geometric setting for studying complex analytic functions and their multi-valued behavior.
-
D.
Kähler manifold
A Kähler manifold is a complex manifold equipped with a Hermitian metric whose associated symplectic form is closed, making it simultaneously a complex, Riemannian, and symplectic manifold in a compatible way.
-
E.
Deligne cohomology
Deligne cohomology is a refined cohomology theory in algebraic geometry that combines singular cohomology and differential forms to capture both topological and arithmetic information about complex algebraic varieties.
- F. None of above. chosen
Statements (39)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ nonfiction work ⓘ |
| describedAs | foundational mathematical monograph that systematically develops the theory of differential and complex geometry on complex manifolds ⓘ |
| field |
complex analysis
ⓘ
complex geometry ⓘ differential geometry ⓘ global analysis ⓘ |
| focus |
interaction between differential geometry and complex analysis
ⓘ
systematic development of differential analysis on complex manifolds ⓘ |
| hasAudience |
graduate students in mathematics
ⓘ
researchers in complex geometry ⓘ researchers in differential geometry ⓘ |
| mathematicalSubjectClassification |
32Qxx
ⓘ
53Cxx ⓘ |
| topic |
∂-Neumann problem
ⓘ
Bochner technique ⓘ Cauchy–Riemann equations ⓘ Dolbeault cohomology ⓘ
linked to:
Dolbeault cohomology classes
Hermitian metrics ⓘ Hodge theory ⓘ Kähler manifolds ⓘ Laplace operators on complex manifolds ⓘ almost complex structures ⓘ complex manifolds ⓘ complex structures ⓘ connections on vector bundles ⓘ curvature of vector bundles ⓘ differential forms on complex manifolds ⓘ elliptic differential operators ⓘ harmonic forms ⓘ holomorphic vector bundles ⓘ integration on complex manifolds ⓘ line bundles on complex manifolds ⓘ pseudoconvexity ⓘ sheaf cohomology on complex manifolds ⓘ vanishing theorems ⓘ |
| usedAs |
graduate textbook
ⓘ
reference work ⓘ |
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: Differential Analysis on Complex Manifolds Description of subject: "Differential Analysis on Complex Manifolds" is a foundational mathematical monograph that systematically develops the theory of differential and complex geometry on complex manifolds.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.