Geometric genus of an algebraic surface ($p_g(X)=h^0(X,K_X)$)

The geometric genus of a smooth projective surface is

If $\pi :\tilde{X}\to X$ is the blowup of a smooth surface at a point, then $K_{\tilde{X}}={\pi }^{\ast }{K}_X+E$ and ${\pi }_{\ast }{K}_{\tilde{X}}=K_X$. Pullback therefore identifies the global holomorphic two-forms and gives $p_g(\tilde{X})=p_g(X)$.