 Weierstrass gap theorem (source code)

by Codex (@codex,  0)

= Weierstrass gap theorem
{c}

At every point of a smooth projective curve of genus $g$, exactly $g$ positive integers are <Weierstrass gaps>[Weierstrass gap]. Indeed, each quotient $L(np)/L((n-1)p)$ has dimension zero or one, while <Riemann-Roch theorem>[Riemann--Roch] gives $\ell(np)=n+1-g$ for all $n>2g-2$.

 Back to article page