Several Complex Variables
E613412
"Several Complex Variables" is a foundational mathematical text that systematically develops the theory of functions of several complex variables and has significantly influenced modern complex analysis.
All labels observed (2)
| Label | Occurrences |
|---|---|
| "Several Complex Variables" | 1 |
| Several Complex Variables canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6716291 — 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: Several Complex Variables Context triple: [Salomon Bochner, notableWork, Several Complex Variables]
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A.
Fefferman metric in several complex variables
The Fefferman metric in several complex variables is a canonical Lorentz–Kähler-type metric associated with strictly pseudoconvex domains, fundamental in the study of CR geometry and the boundary behavior of holomorphic functions.
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B.
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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C.
Complex Analysis
Complex Analysis is a classic, widely used textbook that provides a rigorous introduction to the theory of functions of a complex variable.
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D.
Lempert function on convex domains
The Lempert function on convex domains is a complex-analytic invariant that coincides with the Kobayashi distance and provides an extremal characterization of holomorphic mappings between convex domains in several complex variables.
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E.
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.
- 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: Several Complex Variables Target entity description: "Several Complex Variables" is a foundational mathematical text that systematically develops the theory of functions of several complex variables and has significantly influenced modern complex analysis.
-
A.
Fefferman metric in several complex variables
The Fefferman metric in several complex variables is a canonical Lorentz–Kähler-type metric associated with strictly pseudoconvex domains, fundamental in the study of CR geometry and the boundary behavior of holomorphic functions.
-
B.
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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C.
Complex Analysis
Complex Analysis is a classic, widely used textbook that provides a rigorous introduction to the theory of functions of a complex variable.
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D.
Lempert function on convex domains
The Lempert function on convex domains is a complex-analytic invariant that coincides with the Kobayashi distance and provides an extremal characterization of holomorphic mappings between convex domains in several complex variables.
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E.
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.
- F. None of above. chosen
Statements (36)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics textbook
ⓘ
monograph ⓘ |
| developsTheoryOf |
Cauchy integral formulas in several variables
ⓘ
linked to:
Bochner–Martinelli formula
Hartogs phenomenon ⓘ Levi problem ⓘ analytic continuation in several variables ⓘ domains of holomorphy ⓘ domains of holomorphy and pseudoconvex domains ⓘ holomorphic functions of several complex variables ⓘ holomorphic mappings between complex domains ⓘ plurisubharmonic functions ⓘ power series in several complex variables ⓘ pseudoconvexity ⓘ |
| hasAudience |
graduate students in mathematics
ⓘ
researchers in complex analysis ⓘ |
| hasField |
complex analysis
ⓘ
functions of several complex variables ⓘ mathematical analysis ⓘ |
| hasImpact |
influenced subsequent textbooks in complex analysis
ⓘ
shaped modern approaches to several complex variables ⓘ |
| hasInfluenceOn | modern complex analysis ⓘ |
| hasSubject |
Cauchy–Riemann equations in several variables
ⓘ
linked to:
Cauchy–Riemann equations
Oka–Cartan theory ⓘ Runge approximation in several variables ⓘ analytic sets in several complex variables ⓘ extension of holomorphic functions ⓘ holomorphic convexity ⓘ local and global properties of analytic functions in several variables ⓘ separate analyticity and joint analyticity ⓘ singularities of holomorphic functions in several variables ⓘ theory of holomorphic functions in C^n ⓘ |
| isCharacterizedBy |
emphasis on foundational aspects of the theory
ⓘ
rigorous exposition ⓘ systematic development of several complex variables ⓘ |
| isFoundationalFor | graduate study in several complex variables ⓘ |
| isUsedAs | reference text in complex analysis ⓘ |
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: Several Complex Variables Description of subject: "Several Complex Variables" is a foundational mathematical text that systematically develops the theory of functions of several complex variables and has significantly influenced modern complex analysis.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Several Complex Variables