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arXiv · 2304.12068

Intersection matrices for the minimal regular model of ${X}_0(N)$ and applications to the Arakelov canonical sheaf

Paolo Dolce·Pietro Mercuri
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Abstract

Let $N>1$ be an integer coprime to $6$ such that $N\notin\{5,7,13\}$ and let $g=g(N)$ be the genus of the modular curve $X_0(N)$. We compute the intersection matrices relative to special fibres of the minimal regular model of $X_0(N)$. Moreover we prove that the self-intersection of the Arakelov canonical sheaf of $X_0(N)$ is asymptotic to $3g\log N$, for $N\to+\infty$.

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Paolo Dolce, Pietro Mercuri. 2023-04-24. Intersection matrices for the minimal regular model of ${X}_0(N)$ and applications to the Arakelov canonical sheaf. https://arxiv.org/abs/2304.12068

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