Vector Bundles on Rational Topologically Contractible Affine Threefolds

Haoyang Liu; Biman Roy

Vector Bundles on Rational Topologically Contractible Affine Threefolds

Algebraic Geometry 2026-07-04 v1

Authors: Haoyang Liu , Biman Roy

Abstract

The generalized Serre question asks whether any algebraic vector bundle over a topologically contractible, smooth, affine, complex variety $X$ is trivial. In this article, we prove an affirmative answer to this question, if the dimension of $X$ is 3 and $X$ is rationally connected. As an example, this proves that every algebraic vector bundle over any Koras-Russell threefold (first or second kind and certain third kind) is trivial.

Keywords

vector bundles Serre's question rationally connected varieties affine threefolds Koras-Russell threefolds algebraic vector bundles

Cite

@article{arxiv.2607.05444,
  title  = {Vector Bundles on Rational Topologically Contractible Affine Threefolds},
  author = {Haoyang Liu and Biman Roy},
  journal= {arXiv preprint arXiv:2607.05444},
  year   = {2026}
}