The construction problem for Hodge numbers

What are the possible Hodge numbers of a smooth complex projective variety? We construct enough varieties to show that many of the Hodge numbers can take all possible values satisfying the constraints given by Hodge theory. For example, there are varieties such that a Hodge number \(h^{p,0}\) is big and the intermediate Hodge numbers \(h^{i,p-i}\) are small.