Colloquium

A projective variety \(X\) over an algebraically closed field \(k\) is the zero-locus of some finite family of homogeneous polynomials with coefficients in \(k\). It turns out that the geometrical (topological) properties of a projective variety are closely related to its algebraic structure of the meromorphic functions — the Kodaira dimension. In this talk, we shall discuss some recent development on the projective varieties with non-positive Kodaira dimension, in particular, the varieties with numerically effective anti-canonical divisor.