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.