Triple
T12220533
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Plücker formulas |
E291201
|
entity |
| Predicate | relatedConcept |
P37
|
FINISHED |
| Object |
Severi varieties
Severi varieties are special projective algebraic varieties characterized by extremal geometric properties, such as having secant varieties of minimal possible dimension, and form a small, highly structured class in algebraic geometry.
|
E969577
|
NE FINISHED |
How this triple was built (4 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Severi varieties | Statement: [Plücker formulas, relatedConcept, Severi varieties]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Severi varieties Context triple: [Plücker formulas, relatedConcept, Severi varieties]
-
A.
Shimura varieties
Shimura varieties are higher-dimensional algebraic varieties that generalize modular curves and play a central role in the Langlands program by connecting number theory, automorphic forms, and arithmetic geometry.
-
B.
Jacobian varieties
Jacobian varieties are complex algebraic varieties associated to algebraic curves that parametrize degree-zero line bundles (or divisor classes) on the curve and carry a natural structure of principally polarized abelian varieties.
-
C.
Kummer surfaces
Kummer surfaces are special quartic algebraic surfaces in projective three-space characterized by having 16 ordinary double points, extensively studied in the context of complex geometry and abelian varieties.
-
D.
Brill–Noether theory
Brill–Noether theory is a branch of algebraic geometry that studies linear series on algebraic curves, particularly the existence and dimension of spaces of special divisors and maps to projective spaces.
-
E.
Hirzebruch surfaces
Hirzebruch surfaces are a family of complex algebraic surfaces that serve as fundamental examples in algebraic geometry and the classification of complex surfaces.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Severi varieties Triple: [Plücker formulas, relatedConcept, Severi varieties]
Generated description
Severi varieties are special projective algebraic varieties characterized by extremal geometric properties, such as having secant varieties of minimal possible dimension, and form a small, highly structured class in algebraic geometry.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Severi varieties Target entity description: Severi varieties are special projective algebraic varieties characterized by extremal geometric properties, such as having secant varieties of minimal possible dimension, and form a small, highly structured class in algebraic geometry.
-
A.
Shimura varieties
Shimura varieties are higher-dimensional algebraic varieties that generalize modular curves and play a central role in the Langlands program by connecting number theory, automorphic forms, and arithmetic geometry.
-
B.
Jacobian varieties
Jacobian varieties are complex algebraic varieties associated to algebraic curves that parametrize degree-zero line bundles (or divisor classes) on the curve and carry a natural structure of principally polarized abelian varieties.
-
C.
Kummer surfaces
Kummer surfaces are special quartic algebraic surfaces in projective three-space characterized by having 16 ordinary double points, extensively studied in the context of complex geometry and abelian varieties.
-
D.
Brill–Noether theory
Brill–Noether theory is a branch of algebraic geometry that studies linear series on algebraic curves, particularly the existence and dimension of spaces of special divisors and maps to projective spaces.
-
E.
Hirzebruch surfaces
Hirzebruch surfaces are a family of complex algebraic surfaces that serve as fundamental examples in algebraic geometry and the classification of complex surfaces.
- F. None of above. chosen
Provenance (5 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69d6ab668acc8190963ba424049d6aee |
completed | April 8, 2026, 7:24 p.m. |
| NER | Named-entity recognition | batch_69d91c951f5881908db6edfda1153d6f |
completed | April 10, 2026, 3:51 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f60aa4f4388190a787dde12190c51a |
completed | May 2, 2026, 2:31 p.m. |
| NEDg | Description generation | batch_69f60bdca250819090b4b4cc84d343f4 |
completed | May 2, 2026, 2:36 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69f60cd51d34819099927fee476958ea |
completed | May 2, 2026, 2:40 p.m. |
Created at: April 8, 2026, 9:51 p.m.