Petri’s theorem
E898504
Petri’s theorem is a fundamental result in algebraic geometry that characterizes the ideal of a canonically embedded algebraic curve by describing it as being generated by quadrics under suitable conditions.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Petri’s theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10992029 — 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: Petri’s theorem Context triple: [Brill–Noether theory, relatedTo, Petri’s theorem]
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A.
Kesten’s theorem
Kesten’s theorem is a fundamental result in probability theory that characterizes when a random walk on a group is transient or recurrent, with deep implications for random walks on groups and percolation theory.
-
B.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
-
C.
Rabin–Scott powerset construction
The Rabin–Scott powerset construction is a fundamental algorithm in automata theory that converts nondeterministic finite automata (NFAs) into equivalent deterministic finite automata (DFAs) by using sets of states as single states.
-
D.
Page theorem
The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
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E.
Tarski’s fixed point theorem
Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
- 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: Petri’s theorem Target entity description: Petri’s theorem is a fundamental result in algebraic geometry that characterizes the ideal of a canonically embedded algebraic curve by describing it as being generated by quadrics under suitable conditions.
-
A.
Kesten’s theorem
Kesten’s theorem is a fundamental result in probability theory that characterizes when a random walk on a group is transient or recurrent, with deep implications for random walks on groups and percolation theory.
-
B.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
-
C.
Rabin–Scott powerset construction
The Rabin–Scott powerset construction is a fundamental algorithm in automata theory that converts nondeterministic finite automata (NFAs) into equivalent deterministic finite automata (DFAs) by using sets of states as single states.
-
D.
Page theorem
The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
-
E.
Tarski’s fixed point theorem
Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
- F. None of above. chosen
Statements (36)
| Predicate | Object |
|---|---|
| instanceOf |
result in the theory of algebraic curves
ⓘ
theorem in algebraic geometry ⓘ |
| appliesTo |
canonically embedded curves
ⓘ
non-hyperelliptic curves ⓘ smooth projective curves ⓘ |
| asserts | for a non-hyperelliptic smooth projective curve of genus g ≥ 3, the canonical ideal is generated by quadrics except for certain special cases ⓘ |
| characterizes | canonical ideal of a curve in terms of quadrics ⓘ |
| concerns |
canonical embeddings of algebraic curves
ⓘ
canonical models of curves ⓘ homogeneous ideal of a canonically embedded curve ⓘ |
| describes | generators of the canonical ideal of a non-hyperelliptic curve ⓘ |
| field |
algebraic geometry
ⓘ
theory of algebraic curves ⓘ |
| hasCondition |
curve must be non-hyperelliptic
ⓘ
curve must be projective ⓘ curve must be smooth ⓘ genus at least 3 ⓘ |
| hasException |
certain special linear series on curves
ⓘ
plane quintic curves ⓘ trigonal curves ⓘ |
| hasGeneralization |
Green–Lazarsfeld results on syzygies
ⓘ
results on higher syzygies of canonical curves ⓘ |
| historicalPeriod | early 20th century mathematics ⓘ |
| implies | projective normality of the canonical embedding under its hypotheses ⓘ |
| namedAfter | Karl Petri ⓘ |
| relatedTo |
Brill–Noether theory
ⓘ
Green’s conjecture on syzygies of canonical curves ⓘ
linked to:
Green’s conjecture
canonical linear system of a curve ⓘ projective normality of canonical curves ⓘ syzygies of canonical curves ⓘ |
| standardReference |
classical textbooks on algebraic curves
ⓘ
modern treatments of canonical curves and syzygies ⓘ |
| states | the canonical ideal is generated by quadrics for a general non-hyperelliptic curve of genus g ≥ 3 ⓘ |
| usedIn |
analysis of generators and relations of canonical rings
ⓘ
classification of algebraic curves by their canonical models ⓘ study of special linear series on curves ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Petri’s theorem Description of subject: Petri’s theorem is a fundamental result in algebraic geometry that characterizes the ideal of a canonically embedded algebraic curve by describing it as being generated by quadrics under suitable conditions.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.