The Miyaoka-Yau inequality and uniformisation of canonical models

Abstract

We establish the Miyaoka-Yau inequality in terms of orbifold Chern classes for the tangent sheaf of any complex projective variety of general type with klt singularities and nef canonical divisor. In case equality is attained for a variety with at worst terminal singularities, we prove that the associated canonical model is the quotient of the unit ball by a discrete group action.

v3: final version, added section on "Further directions"; accepted for publication by Annales scientifiques de l'Ecole normale supérieure

References in corpus (1)

• Orbifold Stability and Miyaoka-Yau Inequality for minimal pairs

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• Uniformisation of higher-dimensional minimal varieties
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