Miyaoka-Yau inequalities and the topological characterization of certain klt varieties

Abstract

Ball quotients, hyperelliptic varieties, and projective spaces are characterized by their Chern classes, as the varieties where the Miyaoka-Yau inequality becomes an equality. Ball quotients, Abelian varieties, and projective spaces are also characterized topologically: if a complex, projective manifold $X$ is homeomorphic to a variety of this type, then $X$ is itself of this type. In this paper, similar results are established for projective varieties with klt singularities that are homeomorphic to singular ball quotients, quotients of Abelian varieties, or projective spaces.

arXiv comment16 pages; v2: minimal changes, accepted for publication in the special volume of Comptes Rendus Mathématique in memory of Jean-Pierre Demailly

References in corpus (10)

• Differential Forms on Log Canonical Spaces
• Étale fundamental groups of Kawamata log terminal spaces, flat sheaves, and quotients of Abelian varieties
• The Miyaoka-Yau inequality and uniformisation of canonical models
• Projective flatness over klt spaces and uniformisation of varieties with nef anti-canonical divisor
• Nakamaye's theorem on complex manifolds
• Harmonic metrics on Higgs sheaves and uniformization of varieties of general type
• A characterization of finite quotients of Abelian varieties
• Minimal model program for projective morphisms between complex analytic spaces
• Vanishing theorems for projective morphisms between complex analytic spaces
• Equality in the Miyaoka-Yau inequality and uniformization of non-positively curved klt pairs