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arXiv · 2212.11530

Locally Constant Fibrations and Positivity of Curvature

Niklas Müller
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Abstract

Up to finite étale cover, any smooth complex projective variety $X$ with nef anti-canonical bundle is a holomorphic fibre bundle over a $K$-trivial variety with locally constant transition functions. We show that this result is optimal by proving that any projective fibre bundle with locally constant transition functions over a $K$-trivial variety has a nef anti-canonical bundle. Moreover, we complement some results on the structure theory of varieties whose tangent bundle admits a singular hermitean metric of positive curvature.

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Niklas Müller. 2025-03-25. Locally Constant Fibrations and Positivity of Curvature. https://arxiv.org/abs/2212.11530

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