Triple

T33579732
Position Surface form Disambiguated ID Type / Status
Subject Picard group E860119 entity
Predicate instanceOf P0 FINISHED
Object birational invariant (for smooth projective varieties over a field) C58003 CONCEPT FINISHED

How this triple was built (1 step)

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.

CD Concept disambiguation gpt-5-mini-2025-08-07
Target class: birational invariant (for smooth projective varieties over a field)
Context triple: [Picard group, instanceOf, birational invariant (for smooth projective varieties over a field)]
  • A. object in invariant theory
    An object in invariant theory is a mathematical entity, such as a vector space, polynomial ring, or group action, whose structure and symmetries are studied through the functions or quantities that remain unchanged under a specified group of transformations.
  • B. cohomological invariant chosen
    A cohomological invariant is a rule that assigns to each object in a given class (such as algebraic varieties, groups, or topological spaces) an element of a cohomology group in a way that is functorial and captures structural or classification information about those objects.
  • C. divisor in algebraic geometry
    A divisor in algebraic geometry is a formal finite integer linear combination of irreducible codimension-one subvarieties (or points on a curve), used to encode zeros and poles of rational functions and to study line bundles and linear systems.
  • D. algebraic variety
    An algebraic variety is a geometric object defined as the set of common solutions to a system of polynomial equations over a field, studied up to algebraic and topological properties.
  • E. problem in invariant theory
    A problem in invariant theory concerns determining and characterizing the algebraic functions (invariants) that remain unchanged under the action of a given group on a vector space or algebraic variety.
  • F. None of above.

Provenance (1 batch)

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_69f3497d37848190afcbb5ef3f5c7376 completed April 30, 2026, 12:22 p.m.
Created at: May 1, 2026, 1:40 a.m.