Theorie der algebraischen Kurven
E291204
"Theorie der algebraischen Kurven" is a foundational 19th-century mathematical treatise by Julius Plücker that systematically develops the geometry and classification of algebraic curves.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Theorie der algebraischen Curven | 1 |
| Theorie der algebraischen Kurven canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2689822 — 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: Theorie der algebraischen Kurven Context triple: [Julius Plücker, notableWork, Theorie der algebraischen Kurven]
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A.
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.
-
B.
Theorie der binären algebraischen Formen
"Theorie der binären algebraischen Formen" is a foundational 19th-century mathematical treatise by Alfred Clebsch on the theory of binary algebraic forms and invariants.
-
C.
Die Theorie der algebraischen Zahlkörper
"Die Theorie der algebraischen Zahlkörper" is a foundational mathematical monograph on algebraic number fields, authored by David Hilbert and published as part of his influential Zahlbericht.
-
D.
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.
-
E.
Hurwitz bound on automorphism groups of curves
The Hurwitz bound on automorphism groups of curves is a classical result in algebraic geometry stating that a compact Riemann surface of genus at least 2 has at most 84(g − 1) automorphisms.
- 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: Theorie der algebraischen Kurven Target entity description: "Theorie der algebraischen Kurven" is a foundational 19th-century mathematical treatise by Julius Plücker that systematically develops the geometry and classification of algebraic curves.
-
A.
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.
-
B.
Theorie der binären algebraischen Formen
"Theorie der binären algebraischen Formen" is a foundational 19th-century mathematical treatise by Alfred Clebsch on the theory of binary algebraic forms and invariants.
-
C.
Die Theorie der algebraischen Zahlkörper
"Die Theorie der algebraischen Zahlkörper" is a foundational mathematical monograph on algebraic number fields, authored by David Hilbert and published as part of his influential Zahlbericht.
-
D.
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.
-
E.
Hurwitz bound on automorphism groups of curves
The Hurwitz bound on automorphism groups of curves is a classical result in algebraic geometry stating that a compact Riemann surface of genus at least 2 has at most 84(g − 1) automorphisms.
- F. None of above. chosen
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
geometry book ⓘ mathematical treatise ⓘ nonfiction book ⓘ |
| academicDiscipline | mathematics ⓘ |
| author | Julius Plücker ⓘ |
| authorNationality | German ⓘ |
| authorOfWork | Julius Plücker ⓘ |
| contribution |
early classification of algebraic curves
ⓘ
foundational work in algebraic geometry ⓘ systematic development of the geometry of algebraic curves ⓘ |
| countryOfOrigin | Germany ⓘ |
| field |
algebraic geometry
ⓘ
classical algebraic geometry ⓘ projective geometry ⓘ |
| genre |
mathematics textbook
ⓘ
scientific literature ⓘ |
| hasAuthor | Julius Plücker ⓘ |
| hasForm | printed book ⓘ |
| historicalPeriod | 19th-century mathematics ⓘ |
| influenced | later studies of plane algebraic curves ⓘ |
| influencedField |
algebraic geometry
ⓘ
projective geometry ⓘ |
| intendedAudience |
advanced students of mathematics
ⓘ
mathematicians ⓘ |
| language | German ⓘ |
| mainSubject |
algebraic curves
ⓘ
classification of algebraic curves ⓘ geometry of plane curves ⓘ |
| originalTitle |
Theorie der algebraischen Curven
ⓘ
linked to:
Theorie der algebraischen Kurven
|
| publicationCentury | 19th century ⓘ |
| relatedTo |
Plücker formulas
ⓘ
projective duality of curves ⓘ |
| titleLanguage | de ⓘ |
| topic |
analytic representation of curves
ⓘ
classification by invariants ⓘ degree and order of algebraic curves ⓘ projective properties of curves ⓘ singularities of algebraic curves ⓘ |
| workType | monograph ⓘ |
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: Theorie der algebraischen Kurven Description of subject: "Theorie der algebraischen Kurven" is a foundational 19th-century mathematical treatise by Julius Plücker that systematically develops the geometry and classification of algebraic curves.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Theorie der algebraischen Kurven