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dbr:List_of_algebraic_geometry_topics
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dbr:Brill–Noether_theory
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Brill–Noether theory Diviseur spécial
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En mathématiques, un diviseur spécial est un diviseur sur une courbe algébrique qui possède la particularité de déterminer plus de fonctions compatibles qu'attendu. La condition pour qu'un diviseur D soit spécial peut être formulée en termes de cohomologie des faisceaux comme la non-trivialité du groupe de cohomologie H1 du faisceau des sections du faisceau inversible associé à D. Par le théorème de Riemann-Roch, cela signifie que le groupe de cohomologie H0, espace des sections holomorphes, est plus gros qu'attendu. In algebraic geometry, Brill–Noether theory, introduced by Alexander von Brill and Max Noether, is the study of special divisors, certain divisors on a curve C that determine more compatible functions than would be predicted. In classical language, special divisors move on the curve in a "larger than expected" linear system of divisors. Alternatively, by Serre duality, the condition is that there exist holomorphic differentials with divisor ≥ –D on the curve.
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Alexander Max
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von Brill Noether
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dbo:abstract
In algebraic geometry, Brill–Noether theory, introduced by Alexander von Brill and Max Noether, is the study of special divisors, certain divisors on a curve C that determine more compatible functions than would be predicted. In classical language, special divisors move on the curve in a "larger than expected" linear system of divisors. The condition to be a special divisor D can be formulated in sheaf cohomology terms, as the non-vanishing of the H1 cohomology of the sheaf of the sections of the invertible sheaf or line bundle associated to D. This means that, by the Riemann–Roch theorem, the H0 cohomology or space of holomorphic sections is larger than expected. Alternatively, by Serre duality, the condition is that there exist holomorphic differentials with divisor ≥ –D on the curve. En mathématiques, un diviseur spécial est un diviseur sur une courbe algébrique qui possède la particularité de déterminer plus de fonctions compatibles qu'attendu. La condition pour qu'un diviseur D soit spécial peut être formulée en termes de cohomologie des faisceaux comme la non-trivialité du groupe de cohomologie H1 du faisceau des sections du faisceau inversible associé à D. Par le théorème de Riemann-Roch, cela signifie que le groupe de cohomologie H0, espace des sections holomorphes, est plus gros qu'attendu. Par (en), cette condition se traduit par l'existence de différentielles holomorphes de diviseur ≥ −D sur la courbe.
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Alexander von Brill
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Max Noether
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