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arXiv · 2609.07069

A note on compact Kähler varieties with pseudo-effective tangent sheaf

Shin-ichi Matsumura·Guolei Zhong
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Abstract

In this paper, we discuss recent developments and open problems concerning the geometry of compact Kähler varieties whose tangent sheaves are pseudo-effective in a strong sense. As our main result, we prove that, after passing to a finite quasi-étale cover, any compact Kähler variety with quotient singularities and pseudo-effective tangent sheaf admits a flat fibration onto a complex torus, with rationally connected fibers. We also obtain an analogous structure theorem for klt compact Kähler varieties, assuming the existence of minimal models in numerical dimension zero; consequently, the result holds unconditionally in the projective setting and for low-dimensional compact Kähler varieties.

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Shin-ichi Matsumura, Guolei Zhong. 2026-09-07. A note on compact Kähler varieties with pseudo-effective tangent sheaf. https://arxiv.org/abs/2609.07069

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