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Revision difference : Riemann-Roch theorem for curves |
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Version 3 |
| Let $C$ be a projective nonsingular curve over an algebraically closed field. If $D$ is a divisor on $C$, then |
Let $C$ be a projective nonsingular curve over an algebraically closed field. If $D$ is a divisor on $C$, then |
| $$\ell(D) - \ell(K-D) = {\rm deg}(D) + 1 - g$$ |
$$\ell(D) - \ell(K-D) = {\rm deg}(D) + 1 - g$$ |
| where $g$ is the genus of the curve, and $K$ is the canonical divisor ($\ell(K)=g$). |
where $g$ is the genus of the curve, and $K$ is the canonical divisor ($\ell(K)=g$). |
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