Special Divisor
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High Quality Content by WIKIPEDIA articles! In mathematics, in the theory of algebraic curves, certain divisors on a curve C are particular, in the sense of determining more compatible functions than would be predicted. These are the special divisors. In classical language, they move on the curve in a larger 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 H...
High Quality Content by WIKIPEDIA articles! In mathematics, in the theory of algebraic curves, certain divisors on a curve C are particular, in the sense of determining more compatible functions than would be predicted. These are the special divisors. In classical language, they move on the curve in a larger 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.
