Holomorphic Lie algebroid connections over rationally connected varieties

Indranil Biswas; Anoop Singh

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arXiv · 2605.28256

Holomorphic Lie algebroid connections over rationally connected varieties

Indranil Biswas·Anoop Singh

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Abstract

Take a holomorphic Lie algebroid $(V,\phi)$ over a rationally connected smooth complex projective variety $X$. We show that, under certain conditions, a vector bundle $E$ over $X$ admits a $(V,\phi)$-connection if and only if $E$ is trivial. Moreover, we prove that under the same conditions, any $(V,\phi)$-connection over $X$ is flat.

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Indranil Biswas, Anoop Singh. 2026-05-27. Holomorphic Lie algebroid connections over rationally connected varieties. https://arxiv.org/abs/2605.28256

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