Accola–Maclachlan bound
E904004
The Accola–Maclachlan bound is a refinement in algebraic geometry that gives an improved upper limit on the size of the automorphism group of a compact Riemann surface (or algebraic curve), sharpening the classical Hurwitz bound in certain cases.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Accola–Maclachlan bound canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11085938 — 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: Accola–Maclachlan bound Context triple: [Hurwitz bound on automorphism groups of curves, relatedResult, Accola–Maclachlan bound]
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A.
Barankin bound
The Barankin bound is a fundamental lower bound in statistical estimation theory that generalizes and can be tighter than the Cramér–Rao bound for the variance of unbiased estimators, especially in non-regular or finite-sample settings.
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B.
Alon–Boppana bound
The Alon–Boppana bound is a fundamental result in spectral graph theory that gives an asymptotic lower bound on the second-largest eigenvalue of large regular graphs, showing inherent limitations on how well such graphs can approximate expanders.
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C.
Hamming bound
The Hamming bound is a fundamental limit in coding theory that specifies the maximum number of codewords a block code can have for a given length and minimum distance while still allowing reliable error detection and correction.
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D.
Graham–Pollak theorem
The Graham–Pollak theorem is a result in graph theory that states the edges of a complete graph on n vertices cannot be partitioned into fewer than n−1 complete bipartite subgraphs.
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E.
Cramér–Rao bound
The Cramér–Rao bound is a fundamental result in statistical estimation theory that gives a lower limit on the variance of any unbiased estimator of a parameter, characterizing the best possible precision achievable.
- 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: Accola–Maclachlan bound Target entity description: The Accola–Maclachlan bound is a refinement in algebraic geometry that gives an improved upper limit on the size of the automorphism group of a compact Riemann surface (or algebraic curve), sharpening the classical Hurwitz bound in certain cases.
-
A.
Barankin bound
The Barankin bound is a fundamental lower bound in statistical estimation theory that generalizes and can be tighter than the Cramér–Rao bound for the variance of unbiased estimators, especially in non-regular or finite-sample settings.
-
B.
Alon–Boppana bound
The Alon–Boppana bound is a fundamental result in spectral graph theory that gives an asymptotic lower bound on the second-largest eigenvalue of large regular graphs, showing inherent limitations on how well such graphs can approximate expanders.
-
C.
Hamming bound
The Hamming bound is a fundamental limit in coding theory that specifies the maximum number of codewords a block code can have for a given length and minimum distance while still allowing reliable error detection and correction.
-
D.
Graham–Pollak theorem
The Graham–Pollak theorem is a result in graph theory that states the edges of a complete graph on n vertices cannot be partitioned into fewer than n−1 complete bipartite subgraphs.
-
E.
Cramér–Rao bound
The Cramér–Rao bound is a fundamental result in statistical estimation theory that gives a lower limit on the variance of any unbiased estimator of a parameter, characterizing the best possible precision achievable.
- F. None of above. chosen
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical bound
ⓘ
result in algebraic geometry ⓘ result in the theory of Riemann surfaces ⓘ |
| appliesAlsoTo | smooth projective algebraic curves over algebraically closed fields of characteristic 0 ⓘ |
| appliesTo |
algebraic curves over the complex numbers
ⓘ
automorphism groups of compact Riemann surfaces ⓘ compact Riemann surfaces ⓘ |
| assumes |
compactness of the Riemann surface
ⓘ
genus at least 2 ⓘ |
| comparesWith | Hurwitz bound ⓘ |
| concerns | relationship between genus of a Riemann surface and size of its automorphism group ⓘ |
| context |
finite group actions on Riemann surfaces
ⓘ
maximal automorphism groups of curves of given genus ⓘ |
| expresses | numerical constraint on |Aut(X)| in terms of the genus g of X ⓘ |
| field |
Riemann surface theory
ⓘ
linked to:
Riemann surfaces
algebraic geometry ⓘ automorphism groups of Riemann surfaces ⓘ complex analysis ⓘ group actions on Riemann surfaces ⓘ |
| gives | upper bound on the order of the automorphism group of a compact Riemann surface ⓘ |
| goal | sharpen the general upper bound on automorphism groups beyond Hurwitz’s 84(g−1) bound in special cases ⓘ |
| hasDomain | compact Riemann surfaces of genus g ≥ 2 ⓘ |
| historicalContext | 20th century developments in the theory of Riemann surfaces ⓘ |
| improvesOn | classical Hurwitz bound in certain genera ⓘ |
| involves |
finite groups of conformal automorphisms
ⓘ
hyperbolic geometry of Riemann surfaces ⓘ |
| language |
algebro-geometric formulation
ⓘ
complex analytic formulation ⓘ |
| mathematicalObject | inequality relating genus and automorphism group order ⓘ |
| namedAfter |
Colin Maclachlan
ⓘ
Robert D. M. Accola ⓘ |
| refines | Hurwitz bound ⓘ |
| relatedTo |
Fuchsian groups
ⓘ
Hurwitz surfaces ⓘ automorphism groups of algebraic curves ⓘ uniformization of Riemann surfaces ⓘ |
| typeOf |
group-theoretic bound in geometry
ⓘ
inequality in complex geometry ⓘ |
| usedFor |
classifying Riemann surfaces with large automorphism groups
ⓘ
studying extremal Riemann surfaces with many automorphisms ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Accola–Maclachlan bound Description of subject: The Accola–Maclachlan bound is a refinement in algebraic geometry that gives an improved upper limit on the size of the automorphism group of a compact Riemann surface (or algebraic curve), sharpening the classical Hurwitz bound in certain cases.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.