Geometric genus of an algebraic surface
= Geometric genus of an algebraic surface
{title2=$p_g(X)=h^0(X,K_X)$}
The geometric genus of a smooth projective surface is
$$
p_g(X)=h^0(X,K_X)=h^2(X,\mathcal O_X).
$$
= Geometric genus of an algebraic surface
{title2=$p_g(X)=h^0(X,K_X)$}
The geometric genus of a smooth projective surface is
$$
p_g(X)=h^0(X,K_X)=h^2(X,\mathcal O_X).
$$