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The Miyaoka-Yau inequality and uniformisation of canonical models

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arxiv 1511.08822 v3 pith:VSA657EL submitted 2015-11-27 math.AG

Daniel Greb , Stefan Kebekus , Thomas Peternell , Behrouz Taji This is my paper · ORCID
classification math.AG
keywords canonicalinequalitymiyaoka-yausingularitiesvarietyactionassociatedattained
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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.

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  1. Foliated Minimal Models and Flops

    math.AG 2026-08 conditional novelty 8.0 of 10

    Rank one foliations with canonical singularities have unique minimal models; co-rank one threefolds admit D-flops in klt and F-dlt settings, while new examples show flops and canonical models can fail.

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