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- Hurwitz_surface abstract "In Riemann surface theory and hyperbolic geometry, a Hurwitz surface, named after Adolf Hurwitz, is a compact Riemann surface with precisely 84(g − 1)automorphisms, where g is the genus of the surface. This number is maximal by virtue of Hurwitz's theorem on automorphisms (Hurwitz 1893). They are also referred to as Hurwitz curves, interpreting them as complex algebraic curves (complex dimension 1 = real dimension 2).The Fuchsian group of a Hurwitz surface is a finite index torsionfree normal subgroup of the (ordinary) (2,3,7) triangle group. The finite quotient group is precisely the automorphism group.Automorphisms of complex algebraic curves are orientation-preserving automorphisms of the underlying real surface; if one allows orientation-reversing isometries, this yields a group twice as large, of order 168(g − 1), which is sometimes of interest.A note on terminology – in this and other contexts, the \"(2,3,7) triangle group\" most often refers, not to the full triangle group Δ(2,3,7) (the Coxeter group with Schwarz triangle (2,3,7) or a realization as a hyperbolic reflection group), but rather to the ordinary triangle group (the von Dyck group) D(2,3,7) of orientation-preserving maps (the rotation group), which is index 2. The group of complex automorphisms is a quotient of the ordinary (orientation-preserving) triangle group, while the group of (possibly orientation-reversing) isometries is a quotient of the full triangle group.".
- Hurwitz_surface thumbnail Uniform_tiling_73-t2.png?width=300.
- Hurwitz_surface wikiPageExternalLink 9.html.
- Hurwitz_surface wikiPageExternalLink b44h2sin.pdf.
- Hurwitz_surface wikiPageExternalLink bag44.htm.
- Hurwitz_surface wikiPageExternalLink bag442.
- Hurwitz_surface wikiPageExternalLink bagcon.htm.
- Hurwitz_surface wikiPageID "12807841".
- Hurwitz_surface wikiPageLength "4555".
- Hurwitz_surface wikiPageOutDegree "32".
- Hurwitz_surface wikiPageRevisionID "582670038".
- Hurwitz_surface wikiPageWikiLink (2,3,7)_triangle_group.
- Hurwitz_surface wikiPageWikiLink Adolf_Hurwitz.
- Hurwitz_surface wikiPageWikiLink Algebraic_number_field.
- Hurwitz_surface wikiPageWikiLink Category:Riemann_surfaces.
- Hurwitz_surface wikiPageWikiLink Category:Systolic_geometry.
- Hurwitz_surface wikiPageWikiLink Compact_Riemann_surface.
- Hurwitz_surface wikiPageWikiLink Congruence_subgroup.
- Hurwitz_surface wikiPageWikiLink Coxeter_group.
- Hurwitz_surface wikiPageWikiLink First_Hurwitz_triplet.
- Hurwitz_surface wikiPageWikiLink Fuchsian_group.
- Hurwitz_surface wikiPageWikiLink Genus_(mathematics).
- Hurwitz_surface wikiPageWikiLink Hurwitz_quaternion_order.
- Hurwitz_surface wikiPageWikiLink Hurwitzs_automorphisms_theorem.
- Hurwitz_surface wikiPageWikiLink Hyperbolic_geometry.
- Hurwitz_surface wikiPageWikiLink Index_of_a_subgroup.
- Hurwitz_surface wikiPageWikiLink Klein_quartic.
- Hurwitz_surface wikiPageWikiLink Macbeath_surface.
- Hurwitz_surface wikiPageWikiLink Mathematische_Annalen.
- Hurwitz_surface wikiPageWikiLink Mikhail_Katz.
- Hurwitz_surface wikiPageWikiLink Orientation_(vector_space).
- Hurwitz_surface wikiPageWikiLink PSL(2,7).
- Hurwitz_surface wikiPageWikiLink Prime_ideal.
- Hurwitz_surface wikiPageWikiLink Projective_linear_group.
- Hurwitz_surface wikiPageWikiLink Reflection_group.
- Hurwitz_surface wikiPageWikiLink Riemann_surface.
- Hurwitz_surface wikiPageWikiLink Ring_of_integers.
- Hurwitz_surface wikiPageWikiLink Schwarz_triangle.
- Hurwitz_surface wikiPageWikiLink Simple_group.
- Hurwitz_surface wikiPageWikiLink Systolic_geometry.
- Hurwitz_surface wikiPageWikiLink Triangle_group.
- Hurwitz_surface wikiPageWikiLink File:Uniform_tiling_73-t2.png.
- Hurwitz_surface wikiPageWikiLinkText "Hurwitz surface".
- Hurwitz_surface wikiPageUsesTemplate Template:Algebraic_curves_navbox.
- Hurwitz_surface wikiPageUsesTemplate Template:Arxiv.
- Hurwitz_surface wikiPageUsesTemplate Template:Cite_journal.
- Hurwitz_surface wikiPageUsesTemplate Template:Harv.
- Hurwitz_surface wikiPageUsesTemplate Template:Refbegin.
- Hurwitz_surface wikiPageUsesTemplate Template:Refend.
- Hurwitz_surface wikiPageUsesTemplate Template:Reflist.
- Hurwitz_surface subject Category:Riemann_surfaces.
- Hurwitz_surface subject Category:Systolic_geometry.
- Hurwitz_surface hypernym Surface.
- Hurwitz_surface type Bone.
- Hurwitz_surface type Redirect.
- Hurwitz_surface type Surface.
- Hurwitz_surface comment "In Riemann surface theory and hyperbolic geometry, a Hurwitz surface, named after Adolf Hurwitz, is a compact Riemann surface with precisely 84(g − 1)automorphisms, where g is the genus of the surface. This number is maximal by virtue of Hurwitz's theorem on automorphisms (Hurwitz 1893).".
- Hurwitz_surface label "Hurwitz surface".
- Hurwitz_surface sameAs Q5948842.
- Hurwitz_surface sameAs m.02x5r6s.
- Hurwitz_surface sameAs Поверхность_Гурвица.
- Hurwitz_surface sameAs Hurwitzeva_ploskev.
- Hurwitz_surface sameAs Q5948842.
- Hurwitz_surface sameAs 赫爾維茨曲面.
- Hurwitz_surface wasDerivedFrom Hurwitz_surface?oldid=582670038.
- Hurwitz_surface depiction Uniform_tiling_73-t2.png.
- Hurwitz_surface isPrimaryTopicOf Hurwitz_surface.