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Concept information

geometry > algebraic geometry > Riemann-Roch theorem
mathematical analysis > complex analysis > Riemann-Roch theorem
... > topology > algebraic topology > manifold > differentiable manifold > complex manifold > Riemann surface > Riemann-Roch theorem
... > geometry > topological space > manifold > differentiable manifold > complex manifold > Riemann surface > Riemann-Roch theorem
... > geometry > differential geometry > differentiable manifold > complex manifold > Riemann surface > Riemann-Roch theorem
... > topology > differential topology > differentiable manifold > complex manifold > Riemann surface > Riemann-Roch theorem
geometry > complex geometry > complex manifold > Riemann surface > Riemann-Roch theorem

Preferred term

Riemann-Roch theorem  

Definition

  • The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles. It relates the complex analysis of a connected compact Riemann surface with the surface's purely topological genus g, in a way that can be carried over into purely algebraic settings.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Riemann%E2%80%93Roch_theorem)

Broader concept

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http://data.loterre.fr/ark:/67375/PSR-PBCDPN1D-0

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RDF/XML TURTLE JSON-LD Created 7/21/23, last modified 8/24/23