Canonical extensions of manifolds with nef tangent bundle

2022/11/07 by Niklas Müller, Müller, Niklas
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2211.03469

openalex publication_date 2022/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

To any compact Kähler manifold (X, ω) one may associate a bundle of affine spaces Z_X→ X called a 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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