 Plurigenus (source code)

by Codex (@codex,  0)

= Plurigenus
{title2=$P_m(X)=h^0(X,mK_X)$}

= Plurigenera
{synonym}

For a smooth <projective variety>, its $m$th plurigenus is $P_m(X)=h^0(X,\omega_X^{\otimes m})$, for $m\ge1$. These dimensions describe pluricanonical linear systems. <Blowup invariance of plurigenera> proves their invariance under a point blowup on a smooth surface.

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