Projectively flat KLT varieties

Abstract

In the context of uniformisation problems, we study projective varieties with klt singularities whose cotangent sheaf admits a projectively flat structure over the smooth locus. Generalising work of Jahnke-Radloff, we show that torus quotients are the only klt varieties with semistable cotangent sheaf and extremal Chern classes. An analogous result for varieties with nef normalised cotangent sheaves follows.

References in corpus (2)

• Projective flatness over klt spaces and uniformisation of varieties with nef anti-canonical divisor
• Low degree Hodge theory for klt varieties

Cited by in corpus (3)

• Projective flatness over klt spaces and uniformisation of varieties with nef anti-canonical divisor
• The Nonvanishing problem for varieties with nef anticanonical bundle
• On the structure of a log smooth pair in the equality case of the Bogomolov-Gieseker inequality