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arXiv · 2211.03469

Canonical extensions of manifolds with nef tangent bundle

Niklas Müller
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Abstract

To any compact K\"ahler manifold $(X, \omega)$ one may associate a bundle of affine spaces $Z_X\rightarrow X$ called a \emph{canonical extension} of $X$. In this paper we prove that if the tangent bundle of $X$ is nef, then the total space $Z_X$ 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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Niklas Müller. 2022-11-07. Canonical extensions of manifolds with nef tangent bundle. https://arxiv.org/abs/2211.03469

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