Inequalities of Miyaoka-Yau-type and Uniformisation of Minimal Varieties of intermediate Kodaira Dimension

In this thesis, we prove that the Chern classes of a minimal projective variety X of dimension n and numerical dimension ν always satisfy a certain set of inequalities. In the cases where ν is either very small or very large compared with n, this recovers many previously known results. On the other hand, for intermediate values of ν, our results are completely new. We demonstrate that the inequality we present is sharp by providing an explicit characterisation of those varieties achieving the equality; our proof, in particular, resolves the Abundance conjecture in this situation. Additionally, we provide some new examples of varieties with extremal Chern classes that demonstrate the optimality of our results.