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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Projective flatness over klt spaces and uniformisation of varieties with nef anti-canonical divisor

Authors: Daniel Greb, Stefan Kebekus and Thomas Peternell
Journal: J. Algebraic Geom. 31 (2022), 467-496
Published electronically: March 8, 2022
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Abstract | References | Additional Information

Abstract: We give a criterion for the projectivisation of a reflexive sheaf on a klt space to be induced by a projective representation of the fundamental group of the smooth locus. This criterion is then applied to give a characterisation of finite quotients of projective spaces and Abelian varieties by $\mathbb {Q}$-Chern class (in)equalities and a suitable stability condition. This stability condition is formulated in terms of a naturally defined extension of the tangent sheaf by the structure sheaf. We further examine cases in which this stability condition is satisfied, comparing it to K-semistability and related notions.

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Additional Information

Daniel Greb
Affiliation: Essener Seminar für Algebraische Geometrie und Arithmetik, Fakultät für Mathematik, Universität Duisburg–Essen, 45117 Essen, Germany
MR Author ID: 888778

Stefan Kebekus
Affiliation: Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Ernst-Zermelo-Straße 1, 79104 Freiburg im Breisgau, Germany; and Freiburg Institute for Advanced Studies (FRIAS), Freiburg im Breisgau, Germany
MR Author ID: 637173

Thomas Peternell
Affiliation: Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany
MR Author ID: 138450

Received by editor(s): June 18, 2020
Published electronically: March 8, 2022
Additional Notes: The second author gratefully acknowledges partial support through a fellowship of the Freiburg Institute of Advanced Studies (FRIAS)
Article copyright: © Copyright 2022 University Press, Inc.