Uniformisation of higher-dimensional minimal varieties

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.

29 pages, accepted for publication in the proceedings of the 2015 AMS Summer Institute in Algebraic Geometry, Salt Lake City

References in corpus (5)

• On G-Fano threefolds
• Cohomological characterizations of projective spaces and hyperquadrics
• The Miyaoka-Yau inequality and uniformisation of canonical models
• The structure of surfaces mapping to the moduli stack of canonically polarized varieties
• Shokurov's Rational Connectedness Conjecture

Cited by in corpus (1)

• Projectively flat KLT varieties