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

2023/05/06 by Claudon, Benoît, Graf, Patrick, Guenancia, Henri · 2 citations
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.04074

Abstract

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

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• Beauville-Bogomolov decomposition for klt varieties
• A note on orbifold regularity of canonical metrics

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