Uniformisation of higher-dimensional minimal varieties
Daniel Greb, Stefan Kebekus, Behrouz Taji
TL;DR
This paper reviews classical and modern uniformisation results for complex varieties, introduces key concepts, and sketches recent theorems on uniformisation of singular higher-dimensional varieties.
Contribution
It presents new uniformisation theorems for singular higher-dimensional varieties, expanding the understanding of complex uniformisation beyond smooth cases.
Findings
Recent uniformisation theorems for singular varieties
Introduction of basic technical concepts in higher-dimensional uniformisation
Sketch of proof ideas for the new theorems
Abstract
After a historical discussion of classical uniformisation results for Riemann surfaces, of problems appearing in higher dimensions, and of uniformisation results for projective manifolds with trivial or ample canonical bundle, we introduce the basic technical concepts and sketch the ideas of the proofs for recent uniformisation theorems for singular varieties obtained by the authors in collaboration with Thomas Peternell.
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