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arXiv · 2001.06078

Freeness alone is insufficient for Manin-Peyre

Will Sawin
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Abstract

Manin's conjecture predicts the number of rational points of bounded height on a Fano variety. To make this prediction precise, it is necessary to remove a thin subset of rational points. Peyre has tentatively proposed replacing this subset by the set of points where a certain freeness function he defined takes small values. We show that this proposal fails in the case of $\operatorname{Hilb}^2(\mathbb P^n)$, because the usual thin subset, consisting of rational points that lift to a certain double cover, contains many points with relatively large freeness.

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Will Sawin. 2020-01-16. Freeness alone is insufficient for Manin-Peyre. https://arxiv.org/abs/2001.06078

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