The Miyaoka-Yau inequality and uniformisation of canonical models

• DOI: 10.24033/asens.2414
• Publication Date: 2020-03-11T20:02:04Z
• Authors: Daniel GREB; Stefan KEBEKUS; Thomas PETERNELL; Behrouz TAJI
• Keywords: Orbifold; Sheaf; Calabi–Yau manifold

We establish the Miyaoka-Yau inequality in terms of orbifold Chern classes for tangent sheaf any complex projective variety general type with klt singularities and nef canonical divisor.In case equality is a ained at worst terminal singularities, we prove that associated model quotient unit ball by discrete group action.C 1. Introduction 1 2. Notation standard facts 5 Part I. Foundational material 9 3. Q-varieties Q-Chern 4. Sheaves operators 16 5.Higgs sheaves 19 II.Miyaoka-Yau Inequality Uniformisation 31 6. e Q-Bogomolov-Gieseker 7. Q-Miyaoka-Yau 33 8. 34 9. Characterisation singular quotients 37 10.Further directions 40 III.Appendices Appendix A. restriction theorem References 43 1.IA classical result geometry asserts holomorphic, slope-semistable vector bundle E rank r on compact Kähler manifold (X , ω)