Projectively flat klt varieties
Copyright policy )Projectively flat klt varieties
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.
- University of Freiburg Germany
Mathematics - Differential Geometry, Miyaoka-Yau inequality, uniformisation, abelian variety, Mathematics - Complex Variables, Projective connections, Bogomolov-Gieseker inequality, Coverings in algebraic geometry, stability, 510, klt singularities, projective flatness, Mathematics - Algebraic Geometry, Differential Geometry (math.DG), Notions of stability for complex manifolds, 32Q30, 32Q26, 14E20, 14E30, 53B10, Uniformization of complex manifolds, FOS: Mathematics, Complex Variables (math.CV), Minimal model program (Mori theory, extremal rays), Algebraic Geometry (math.AG)
Mathematics - Differential Geometry, Miyaoka-Yau inequality, uniformisation, abelian variety, Mathematics - Complex Variables, Projective connections, Bogomolov-Gieseker inequality, Coverings in algebraic geometry, stability, 510, klt singularities, projective flatness, Mathematics - Algebraic Geometry, Differential Geometry (math.DG), Notions of stability for complex manifolds, 32Q30, 32Q26, 14E20, 14E30, 53B10, Uniformization of complex manifolds, FOS: Mathematics, Complex Variables (math.CV), Minimal model program (Mori theory, extremal rays), Algebraic Geometry (math.AG)
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