Canonical extensions of manifolds with nef tangent bundle
Niklas M\"uller

TL;DR
This paper proves that for compact Kähler manifolds with nef tangent bundle, their canonical extension is Stein, providing partial answers to a question about the relationship between these properties.
Contribution
It establishes that the canonical extension of a Kähler manifold with nef tangent bundle is Stein, advancing understanding of the geometric structure of such manifolds.
Findings
Canonical extension is Stein for manifolds with nef tangent bundle
Partially answers Greb-Wong's question on equivalence of properties
Provides additional results for surfaces in the converse direction
Abstract
To any compact K\"ahler manifold one may associate a bundle of affine spaces called a \emph{canonical extension} of . In this paper we prove that if the tangent bundle of is nef, then the total space is a Stein manifold. This partially answers a question raised by Greb-Wong of whether these two properties are actually equivalent. We also complement some known results for surfaces in the converse direction.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Geometric and Algebraic Topology
