Elliptic ruled surfaces over arbitrary characteristic fields

Takato Togashi; Hokuto Uehara

Elliptic ruled surfaces over arbitrary characteristic fields

Algebraic Geometry 2022-12-02 v1

Authors: Takato Togashi , Hokuto Uehara

Abstract

Atiyah classifies vector bundles on elliptic curves $E$ over an algebraically closed field of any characteristic. On the other hand, a rank $2$ vector bundle on $E$ defines a surface $S$ with a $\mathbb{P}^1$ -bundle structure on $E$ . We study when $S$ has an elliptic fibration according to the Atiyah's classification, and what kinds of singular fibers appear.

Keywords

vector bundles bundle theory fibrations

Cite

@article{arxiv.2212.00304,
  title  = {Elliptic ruled surfaces over arbitrary characteristic fields},
  author = {Takato Togashi and Hokuto Uehara},
  journal= {arXiv preprint arXiv:2212.00304},
  year   = {2022}
}

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