Mathematics

Let X be a smooth projective variety over the field of complex numbers. X is said to be of general type if and only if the canonical bundle is big. In this talk, we will give a new characterization of varieties of general type via a specific birational invariant, the pseudo-effective dimension of X. In particular, we will prove that X is of general type if and only if the restriction of the canonical divisor of X to any moving curve C is ample.