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

Author:

Benoît Claudon, Patrick Graf, Henri Guenancia

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Complex Variables (math.CV), Differential Geometry (math.DG)

journal:

date:

2023-05-05 16:00:00

Abstract

Let $(X, \Delta)$ be a compact K\"ahler 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).

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