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arXiv · 2211.03397

On integral points of some Fano Threefolds and their Hilbert schemes of lines and conics

Pietro Corvaja·Francesco Zucconi
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Abstract

Let $X^o=\mathbb P^3\setminus D$ where $D$ is the union of two quadrics such that their intersection contains a smooth conic, or the union of a smooth quadric surface and two planes, or the union of a smooth cubic surface $V$ and a plane $\Pi$ such that the intersection $V\cap\Pi$ contains a line. In all these cases we show that the set of integral points of $X^o$ is potentially dense. We apply the above results to prove that integral points are potentially dense in some log-Fano or in some log-Calabi-Yau threefold.

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Pietro Corvaja, Francesco Zucconi. 2022-11-07. On integral points of some Fano Threefolds and their Hilbert schemes of lines and conics. https://arxiv.org/abs/2211.03397

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