Intersection matrices for the minimal regular model of X0(N)${X}_0(N)$ and applications to the Arakelov canonical sheaf

Abstract

Let be an integer coprime to 6 such that and let be the genus of the modular curve . We compute the intersection matrices relative to special fibres of the minimal regular model of . Moreover, we prove that the self‐intersection of the Arakelov canonical sheaf of is asymptotic to , for .