Equality in the Miyaoka-Yau inequality and uniformization of non-positively curved klt pairs

Abstract

Let $(X,\Delta )$ be a compact Kähler klt pair, where $K_X+\Delta$ is ample or numerically trivial, and $\Delta$ has standard coefficients. We show that if equality holds in the orbifold Miyaoka-Yau inequality for $(X,\Delta )$, then its orbifold universal cover is either the unit ball (ample case) or the affine space (numerically trivial case).

References in corpus (3)

• Generic positivity and applications to hyperbolicity of moduli spaces
• Instantons and framed sheaves on Kähler Deligne-Mumford stacks
• Minimal model program for projective morphisms between complex analytic spaces

Cited by in corpus (1)

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