Singular Points of Complex Hypersurfaces
E265524
"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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Singular Points of Complex Hypersurfaces canonical | 2 |
| Les singularités des applications différentiables | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2418335 — 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: Singular Points of Complex Hypersurfaces Context triple: [John Milnor, hasWritten, Singular Points of Complex Hypersurfaces]
-
A.
Hilbert’s fourteenth problem
Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
-
B.
Clebsch diagonal surfaces
Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
-
C.
Sur les courbes algébriques et les variétés qui s’en déduisent
Sur les courbes algébriques et les variétés qui s’en déduisent is a foundational 1948 monograph by André Weil that helped establish modern algebraic geometry and introduced key ideas leading to the Weil conjectures.
-
D.
Éléments de géométrie algébrique
Éléments de géométrie algébrique is a foundational multi-volume treatise that reshaped modern algebraic geometry by developing the theory of schemes and cohomology in a highly general, abstract framework.
-
E.
Hilbert’s Nullstellensatz
Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra 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: Singular Points of Complex Hypersurfaces Target entity description: "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.
-
A.
Hilbert’s fourteenth problem
Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
-
B.
Clebsch diagonal surfaces
Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
-
C.
Sur les courbes algébriques et les variétés qui s’en déduisent
Sur les courbes algébriques et les variétés qui s’en déduisent is a foundational 1948 monograph by André Weil that helped establish modern algebraic geometry and introduced key ideas leading to the Weil conjectures.
-
D.
Éléments de géométrie algébrique
Éléments de géométrie algébrique is a foundational multi-volume treatise that reshaped modern algebraic geometry by developing the theory of schemes and cohomology in a highly general, abstract framework.
-
E.
Hilbert’s Nullstellensatz
Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
monograph ⓘ nonfiction book ⓘ research monograph ⓘ |
| audience |
graduate students in mathematics
ⓘ
researchers in algebraic geometry ⓘ researchers in complex analytic geometry ⓘ researchers in singularity theory ⓘ |
| covers |
classification of simple singularities
ⓘ
deformation theory of hypersurface singularities ⓘ local structure of hypersurface singularities ⓘ stratifications related to singularities ⓘ topology of the Milnor fiber ⓘ |
| describedAs |
foundational monograph in singularity theory
ⓘ
systematic study of singular points of complex hypersurfaces ⓘ |
| field |
algebraic geometry
ⓘ
complex analytic geometry ⓘ complex geometry ⓘ singularity theory ⓘ topology ⓘ |
| focus |
complex algebraic hypersurfaces
ⓘ
complex analytic hypersurfaces ⓘ |
| hasForm | textbook-style exposition ⓘ |
| hasLanguage | English ⓘ |
| hasPerspective | both algebraic and analytic approaches to singularities ⓘ |
| mainSubject |
Milnor fibration
ⓘ
Milnor number ⓘ analytic invariants of singularities ⓘ deformations of singularities ⓘ embedded topological type of singularities ⓘ equisingularity ⓘ isolated hypersurface singularities ⓘ link of a singularity ⓘ local properties of singularities ⓘ monodromy of singularities ⓘ resolution of singularities ⓘ singularities of complex hypersurfaces ⓘ topological invariants of singularities ⓘ topological properties of singularities ⓘ topology of complex hypersurfaces ⓘ vanishing cycles ⓘ |
| topic |
hypersurface singularities in several complex variables
ⓘ
invariants of isolated singularities ⓘ local algebra of singularities ⓘ topological classification of singularities ⓘ |
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: Singular Points of Complex Hypersurfaces Description of subject: "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.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Les singularités des applications différentiables