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arXiv · 2212.00304

Elliptic ruled surfaces over arbitrary characteristic fields

Takato Togashi·Hokuto Uehara
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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.

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Takato Togashi, Hokuto Uehara. 2022-12-01. Elliptic ruled surfaces over arbitrary characteristic fields. https://arxiv.org/abs/2212.00304

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