Given a projective algebraic variety $X$ and a line bundle $L\to X$ the Kodaira-Itaka dimension of $L$ is defined to be the supremum of the dimensions of the image of $X$ by the map $\varphi_{|mL|}$ associated to the linear system $|mL|$ when $m$ is a positive integer, namely $$ \kappa(L)=\sup_{m\in\mathbb N}\{\dim\varphi_{|mL|}(X)\}. $$

It is a standard fact that if we consider the graded ring $$ R(X,L)=\bigoplus_{m\in\mathbb N}H^0(X,mL), $$ then ${tr.deg} R(X,L)=\kappa(L)+1$

When the line bundle we have is the canonical bundle $K_X$ of $X$ then its Kodaira-Itaka dimension is called Kodaira dimension of $X$

In paticular, if for some $m$ we have $\dim\varphi_{|mL|}(X)=\dim X$ then $\kappa(L)=\dim X$ and $L$ is called big.

If $\kappa(X)=\kappa(K_X)=\dim X$ then $X$ is said to be of general type.