About: Hurwitz's automorphisms theorem

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In mathematics, Hurwitz's automorphisms theorem bounds the order of the group of automorphisms, via orientation-preserving conformal mappings, of a compact Riemann surface of genus g > 1, stating that the number of such automorphisms cannot exceed 84(g − 1). A group for which the maximum is achieved is called a Hurwitz group, and the corresponding Riemann surface a Hurwitz surface. Because compact Riemann surfaces are synonymous with non-singular complex projective algebraic curves, a Hurwitz surface can also be called a Hurwitz curve. The theorem is named after Adolf Hurwitz, who proved it in.

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rdf:type	yago:WikicatMathematicalTheorems yago:WikicatTheoremsInAlgebraicGeometry yago:WikicatTheoremsInComplexGeometry yago:WikicatTheoremsInGroupTheory yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293
rdfs:label	Satz von Hurwitz über Automorphismengruppen (de) Hurwitz's automorphisms theorem (en) 리만 곡면 자기 동형군 (ko) Теорема Гурвица об автоморфизмах (ru)
rdfs:comment	Der Satz von Hurwitz über Automorphismengruppen (nach Adolf Hurwitz, 1893) ist eine Aussage der Funktionentheorie. Er besagt, dass die Automorphismengruppe einer hyperbolischen kompakten Riemannschen Fläche endlich ist, und gibt eine nur von topologischen Eigenschaften abhängige obere Schranke für deren Größe an. (de) 리만 곡면 이론에서, 리만 곡면의 자기 동형군(自己同型群, 영어: automorphism group)은 정칙 함수이며 그 역함수 또한 정칙 함수가 되는 전단사 자기 함수들로 구성된 군이다. 종수 1 이하에서는 이는 복소수 리 군을 이루지만, 종수 2 이상에서는 이는 유한군이며, 그 크기의 상계는 후르비츠 자기 동형군 정리(영어: Hurwitz automorphism theorem)에 의하여 주어진다. 이 상계를 포화시키는 리만 곡면을 후르비츠 곡면(Hurwitz曲面, 영어: Hurwitz surface)이라고 한다. (ko) In mathematics, Hurwitz's automorphisms theorem bounds the order of the group of automorphisms, via orientation-preserving conformal mappings, of a compact Riemann surface of genus g > 1, stating that the number of such automorphisms cannot exceed 84(g − 1). A group for which the maximum is achieved is called a Hurwitz group, and the corresponding Riemann surface a Hurwitz surface. Because compact Riemann surfaces are synonymous with non-singular complex projective algebraic curves, a Hurwitz surface can also be called a Hurwitz curve. The theorem is named after Adolf Hurwitz, who proved it in. (en) Теорема Гурвица об автоморфизмах ограничивает порядок группы автоморфизмов — сохраняющих ориентацию конформных отображений — компактной римановой поверхности рода g > 1, утверждая, что число таких автоморфизмов не может превышать 84(g − 1). Группа, для которой достигается максимум, называется группой Гурвица, а соответствующая поверхность Римана — поверхностью Гурвица. Поскольку компактные поверхности Римана являются синонимом неособых комплексных проективных алгебраических кривых, поверхность Гурвица может называться также кривой Гурвица. Теорема названа именем Адольфа Гурвица, который доказал её в 1893 году. (ru)
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dcterms:subject	Riemann surfaces Theorems in group theory Theorems in algebraic geometry Theorems in complex geometry
Wikipage page ID	1113637 (xsd:integer)
Wikipage revision ID	1116352369 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Projective special linear group Scalar curvature Monster group Macbeath surface Riemann-Hurwitz formula Riemann surface Lie group (2,3,7) triangle group Riemann surfaces Compact space Mathematics Genus (mathematics) Order-7 triangular tiling Classical group Elliptic curve Gauss–Bonnet theorem Conway group Order-3 heptagonal tiling Fundamental domain Mathematische Annalen Automorphism Theorems in group theory Torus Held group Janko group Lattice (discrete subgroup) Adolf Hurwitz Algebraic curve Alternating group Discrete group Harada–Norton group Tessellation Lefschetz fixed-point theorem Riemannian manifold Hilbert space Covering space Hurwitz surface Hyperbolic space Riemann sphere Theorems in algebraic geometry Theorems in complex geometry Cohomology Differential geometry Automorphism group Group of Lie type Klein quartic Canadian Mathematical Bulletin Ree group Uniformization theorem Unitary group Lyons group Exceptional Lie group Fischer group Rudvalis group Wythoff construction PSL(2,7) Uniform tiling Hodge decomposition Bolza curve Sporadic groups Orientation-preserving Bring curve Mathematical jargon Regular tiling Conformal mapping Thompson group (finite) Genus (topology) Macbeath curve

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