Irregularity of an algebraic surface (source code)

= Irregularity of an algebraic surface
{title2=$q(X)=h^1(X,\mathcal O_X)$}

The irregularity of a smooth projective complex surface is
$$
q(X)=h^1(X,\mathcal O_X)=h^0(X,\Omega_X^1).
$$