Counting Rational Points on the Stacky $\operatorname{Sym}^2\mathbb{P}^1$

John Yin

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arXiv · 2309.14549

Counting Rational Points on the Stacky $\operatorname{Sym}^2\mathbb{P}^1$

John Yin

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Abstract

We prove the weak form of the generalized Batyrev-Manin-Malle conjecture formulated in \cite{ellenberg2021heights} for the stack $\operatorname{Sym}^2\mathbb{P}^1 := (\mathbb{P}^1 \times \mathbb{P}^1)/S_2$, where the $S_2$ action just permutes the two coordinates. In particular, we show that the diagonal $\Delta \subset \operatorname{Sym}^2\mathbb{P}^1$ is an accumulating substack.

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John Yin. 2023-09-25. Counting Rational Points on the Stacky $\operatorname{Sym}^2\mathbb{P}^1$. https://arxiv.org/abs/2309.14549

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