= Holomorphic map between complex manifolds
{title2=$F:M\longrightarrow N$}
= Holomorphic maps between complex manifolds
{synonym}
A map between <complex manifolds> is holomorphic when its local coordinate expression has holomorphic scalar components. For a smooth map, this is equivalent to its differential being complex-linear at every point. These maps compose by the chain rule. For one-dimensional manifolds this reduces to a <holomorphic map> between <Riemann surfaces>; the general definition also applies to multiplication and inversion on a <complex Lie group>.
Back to article page
