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arXiv · 1307.5912

On the rank of the fibres of rational elliptic surfaces

Cecilia Salgado
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Abstract

We consider an elliptic surface $\pi: \mathcal{E}\rightarrow \mathbb{P}^1$ defined over a number field $k$ and study the problem of comparing the rank of the special fibres over $k$ with that of the generic fibre over $k(\mathbb{P}^1)$. We prove, for a large class of rational elliptic surfaces, the existence of infinitely many fibres with rank at least equal to the generic rank plus two.

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Cecilia Salgado. 2013-07-23. On the rank of the fibres of rational elliptic surfaces. https://arxiv.org/abs/1307.5912

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