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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:appliesTo
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algebraic curves
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gptkbp:category
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theorems in algebraic geometry
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gptkbp:field
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gptkb:algebraic_geometry
complex analysis
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gptkbp:firstPublished
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1857
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gptkbp:form
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l(D) - l(K-D) = deg(D) - g + 1
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gptkbp:formedBy
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19th century
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gptkbp:generalizes
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gptkb:Hirzebruch–Riemann–Roch_theorem
gptkb:Grothendieck–Riemann–Roch_theorem
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https://www.w3.org/2000/01/rdf-schema#label
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Riemann–Roch theorem
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gptkbp:influenced
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modern algebraic geometry
theory of Riemann surfaces
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gptkbp:namedAfter
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gptkb:Bernhard_Riemann
gptkb:Gustav_Roch
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gptkbp:publishedIn
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gptkb:Crelle's_Journal
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gptkbp:relatedTo
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divisor theory
genus of a curve
sheaf cohomology
line bundles
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gptkbp:state
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relates the dimension of the space of sections of a line bundle on a curve to the degree of the bundle and the genus of the curve
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gptkbp:bfsParent
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gptkb:algebraic_geometry
gptkb:Atiyah–Singer_index_theorem
gptkb:Algebraic_geometry
gptkb:Hirzebruch–Riemann–Roch_theorem
gptkb:Serre_duality
gptkb:Brill–Noether_theory
gptkb:Bernhard_Riemann
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gptkbp:bfsLayer
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5
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