ADE singularity theory
E911352
ADE singularity theory is a classification framework in singularity theory and Lie theory that organizes certain simple surface singularities and related algebraic structures into three families labeled A, D, and E.
All labels observed (1)
| Label | Occurrences |
|---|---|
| ADE singularity theory canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11219330 — 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: ADE singularity theory Context triple: [Milnor number, usedIn, ADE singularity theory]
-
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.
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B.
Thom–Mather stratification
Thom–Mather stratification is a refined notion of stratification in differential topology that imposes strong regularity and control conditions on how smooth strata fit together, generalizing and strengthening Whitney stratifications.
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C.
Clebsch–Aronhold invariants
The Clebsch–Aronhold invariants are classical algebraic invariants associated with binary forms, particularly quartic forms, that play a key role in invariant theory and the classification of algebraic curves.
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D.
Topological Methods in Algebraic Geometry
Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.
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E.
Hilbert’s sixteenth problem
Hilbert’s sixteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the topology and arrangement of algebraic curves and surfaces, particularly the number and position of their ovals.
- 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: ADE singularity theory Target entity description: ADE singularity theory is a classification framework in singularity theory and Lie theory that organizes certain simple surface singularities and related algebraic structures into three families labeled A, D, and E.
-
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.
Thom–Mather stratification
Thom–Mather stratification is a refined notion of stratification in differential topology that imposes strong regularity and control conditions on how smooth strata fit together, generalizing and strengthening Whitney stratifications.
-
C.
Clebsch–Aronhold invariants
The Clebsch–Aronhold invariants are classical algebraic invariants associated with binary forms, particularly quartic forms, that play a key role in invariant theory and the classification of algebraic curves.
-
D.
Topological Methods in Algebraic Geometry
Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.
-
E.
Hilbert’s sixteenth problem
Hilbert’s sixteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the topology and arrangement of algebraic curves and surfaces, particularly the number and position of their ovals.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
classification scheme
ⓘ
mathematical theory ⓘ |
| alsoKnownAs | ADE classification of singularities ⓘ |
| appliesTo |
complex two-dimensional singularity
ⓘ
hypersurface singularity ⓘ surface singularity ⓘ |
| characterizedBy |
appearance of simply laced Dynkin diagrams
ⓘ
finite classification into A, D, E types ⓘ |
| classifies |
Kleinian singularities
NERFINISHED
ⓘ
rational double points ⓘ simple Lie algebras ⓘ simple surface singularities ⓘ simply laced Dynkin diagrams ⓘ |
| connects |
finite subgroups of SU(2) and simple Lie algebras
ⓘ
singularity theory and Lie theory ⓘ surface singularities and Dynkin diagrams ⓘ |
| field |
Lie theory
ⓘ
singularity theory ⓘ |
| hasFamily |
A-type
ⓘ
D-type ⓘ E-type NERFINISHED ⓘ |
| historicalOrigin | classification of simple surface singularities by Du Val ⓘ |
| includesExample |
A_n singularity
ⓘ
D_n singularity NERFINISHED ⓘ E_6 singularity ⓘ E_7 singularity NERFINISHED ⓘ E_8 singularity ⓘ |
| influencedBy | Lie algebra classification via Dynkin diagrams ⓘ |
| influences | classification of quivers of finite representation type ⓘ |
| involves |
Milnor fiber
ⓘ
intersection form on vanishing cycles ⓘ modality zero singularities ⓘ simple hypersurface singularities ⓘ |
| organizes | simple surface singularities into A, D, E families ⓘ |
| relatedTo |
Coxeter–Dynkin diagram
NERFINISHED
ⓘ
Dynkin diagram NERFINISHED ⓘ McKay correspondence NERFINISHED ⓘ Weyl group NERFINISHED ⓘ finite subgroup of SU(2) ⓘ quiver representation theory ⓘ root system ⓘ simple Lie algebra ⓘ |
| usedIn |
algebraic geometry
ⓘ
mathematical physics ⓘ mirror symmetry ⓘ representation theory ⓘ string theory ⓘ |
| usesNotation | ADE classification NERFINISHED ⓘ |
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: ADE singularity theory Description of subject: ADE singularity theory is a classification framework in singularity theory and Lie theory that organizes certain simple surface singularities and related algebraic structures into three families labeled A, D, and E.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.