Uniformisation of higher-dimensional minimal varieties

Abstract

Part I. Techniques 9 3. Reflexive differentials 9 4. Existence of maximally quasi-étale covers 11 5. Nonabelian Hodge theory 13 6. Higgs sheaves on singular spaces 16 Part II. Proof of the main results 19 7. Characterisation of torus quotients 19 8. Proof of the Miyaoka-Yau inequality 20 9. Characterisation of singular ball quotients 22 References 25 • the Riemann sphere C = C ∪ {∞}, • the complex plane C, • the unit disk D = {z ∈ C | |z| < 1}.