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gptkbp:instanceOf
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gptkb:mathematical_concept
gptkb:Riemannian_manifold
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gptkbp:automorphismGroup
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finite for genus > 1
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gptkbp:class
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gptkb:genus
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gptkbp:dimensions
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1 (complex dimension)
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gptkbp:Euler_characteristic
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2-2g for genus g
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gptkbp:example
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gptkb:Riemann_sphere
complex torus
hyperelliptic curve
algebraic curve over complex numbers
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gptkbp:fundamentalGroup
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depends on genus
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gptkbp:genus
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non-negative integer
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gptkbp:hasAbelianDifferentials
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yes
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gptkbp:hasBettiNumber
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2g for genus g
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gptkbp:hasCanonicalBundle
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yes
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gptkbp:hasDivisorTheory
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yes
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gptkbp:hasHolomorphicDifferentials
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yes
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gptkbp:hasJacobian
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yes
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gptkbp:hasMappingClassGroup
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yes
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gptkbp:hasMeromorphicFunctions
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yes
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gptkbp:hasModuliSpace
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yes
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gptkbp:hasPeriodMatrix
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yes
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gptkbp:hasProperty
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compact
Kähler manifold
connected
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gptkbp:hasSheaf
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sheaf of holomorphic functions
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gptkbp:hasSpinStructure
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yes
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gptkbp:hasThetaFunction
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yes
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https://www.w3.org/2000/01/rdf-schema#label
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compact Riemann surfaces
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gptkbp:includesMetric
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conformal metric
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gptkbp:isAnalyticSpace
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yes
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gptkbp:isClosed
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yes
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gptkbp:isHausdorff
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yes
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gptkbp:isOrientable
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yes
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gptkbp:isSecondCountable
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yes
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gptkbp:isSmooth
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yes
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gptkbp:relatedTo
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gptkb:algebraic_geometry
gptkb:Teichmüller_space
complex analysis
moduli space
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gptkbp:satisfies
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gptkb:Riemann-Roch_theorem
gptkb:Uniformization_theorem
gptkb:Hodge_decomposition
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gptkbp:universalCover
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gptkb:complex_plane
gptkb:Riemann_sphere
gptkb:unit_disk
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gptkbp:bfsParent
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gptkb:Selberg_trace_formula
gptkb:Hurwitz's_automorphisms_theorem
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gptkbp:bfsLayer
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6
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