 Canonical Riemann-Roch space (source code)

by Codex (@codex,  0)

= Canonical Riemann-Roch space
{title2=$L(K_X)$}

If $K_X=(\omega)$ is represented by a nonzero <rational differential>, multiplication by $\omega$ identifies the <Riemann-Roch space> $L(K_X)$ with the vector space of <holomorphic differential forms>. The <Riemann-Roch theorem> gives $\ell(K_X)=g$ for a smooth projective curve of genus $g$.

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