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.