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- Compact_Riemann_surface abstract "In mathematics, a compact Riemann surface is a complex manifold of dimension one that is a compact space. Riemann surfaces are generally classified first into the compact (those that are closed manifolds) and the open (the rest, which from the point of view of complex analysis are very different, being for example Stein manifolds).A compact Riemann surface C that is a connected space is an algebraic curve defined over the complex number field. More precisely, the meromorphic functions on C make up the function field F on the corresponding curve; F is a field extension of the complex numbers of transcendence degree equal to 1. It can in fact be generated by two functions f and g. This is a structural result on the meromorphic functions: there are enough in the sense of separating out the points of C, and any two are algebraically dependent. These facts were known in the nineteenth century (see GAGA for more in this direction).A general compact Riemann surface is therefore a finite disjoint union of complex (non-singular) algebraic curves.".
- Compact_Riemann_surface wikiPageID "1824772".
- Compact_Riemann_surface wikiPageRevisionID "468881586".
- Compact_Riemann_surface hasPhotoCollection Compact_Riemann_surface.
- Compact_Riemann_surface subject Category:Algebraic_curves.
- Compact_Riemann_surface subject Category:Complex_manifolds.
- Compact_Riemann_surface type Artifact100021939.
- Compact_Riemann_surface type ComplexManifolds.
- Compact_Riemann_surface type Conduit103089014.
- Compact_Riemann_surface type Manifold103717750.
- Compact_Riemann_surface type Object100002684.
- Compact_Riemann_surface type Passage103895293.
- Compact_Riemann_surface type PhysicalEntity100001930.
- Compact_Riemann_surface type Pipe103944672.
- Compact_Riemann_surface type Tube104493505.
- Compact_Riemann_surface type Way104564698.
- Compact_Riemann_surface type Whole100003553.
- Compact_Riemann_surface type YagoGeoEntity.
- Compact_Riemann_surface type YagoPermanentlyLocatedEntity.
- Compact_Riemann_surface comment "In mathematics, a compact Riemann surface is a complex manifold of dimension one that is a compact space. Riemann surfaces are generally classified first into the compact (those that are closed manifolds) and the open (the rest, which from the point of view of complex analysis are very different, being for example Stein manifolds).A compact Riemann surface C that is a connected space is an algebraic curve defined over the complex number field.".
- Compact_Riemann_surface label "Compact Riemann surface".
- Compact_Riemann_surface sameAs m.05zw1j.
- Compact_Riemann_surface sameAs Q5155294.
- Compact_Riemann_surface sameAs Q5155294.
- Compact_Riemann_surface sameAs Compact_Riemann_surface.
- Compact_Riemann_surface wasDerivedFrom Compact_Riemann_surface?oldid=468881586.
- Compact_Riemann_surface isPrimaryTopicOf Compact_Riemann_surface.