We show that smooth varieties of general type which are well formed weighted complete intersections Cartier divisors have maximal Hodge level, is, their the rightmost middle numbers do not vanish. this does hold in quasi-smooth case.

In this paper, we prove the cone theorem and the contraction theorem for pairs (X, B), where X is a normal variety and B is an effective R-divisor on X such that KX+B is R-Cartier.