Classification of conic bundles on a rational elliptic surface in any characteristic

Renato Dias Costa

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arXiv · 2206.03549

Classification of conic bundles on a rational elliptic surface in any characteristic

Renato Dias Costa

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Abstract

Let $X$ be a rational elliptic surface with elliptic fibration $\pi:X\to\Bbb{P}^1$ over an algebraically closed field $k$ of any characteristic. Given a conic bundle $\varphi:X\to\Bbb{P}^1$ we use numerical arguments to classify all possible fibers of $\varphi$ and study the interplay between singular fibers of $\pi$ and $\varphi$.

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Renato Dias Costa. 2022-06-07. Classification of conic bundles on a rational elliptic surface in any characteristic. https://arxiv.org/abs/2206.03549

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