Existence of holomorphic Lie algebroid connections in higher dimensions

Indranil Biswas; Anoop Singh

Existence of holomorphic Lie algebroid connections in higher dimensions

Algebraic Geometry 2026-04-08 v1

Authors: Indranil Biswas , Anoop Singh

Abstract

Let $(V, \phi)$ be a holomorphic Lie algebroid over an irreducible smooth complex projective variety $X$ of dimension at least three, and let $E$ be a holomorphic vector bundle on $X$ . We establish a necessary and sufficient condition for the existence of a holomorphic $(V, \phi)$ --connection on $E$ .

Keywords

holomorphic Lie algebroid connection complex projective variety holomorphic vector bundle existence condition higher dimensions

Cite

@article{arxiv.2604.06003,
  title  = {Existence of holomorphic Lie algebroid connections in higher dimensions},
  author = {Indranil Biswas and Anoop Singh},
  journal= {arXiv preprint arXiv:2604.06003},
  year   = {2026}
}

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9 pages

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