On the arithmetic self-intersection number of the dualizing sheaf on arithmetic surfaces

Abstract

We study the arithmetic self-intersection number of the dualizing sheaf on arithmetic surfaces with respect to morphisms of a particular kind. We obtain upper bounds for the arithmetic self-intersection number of the dualizing sheaf on minimal regular models of the modular curves associated with congruence subgroups ${\Gamma }_0(N)$ with square free level, as well as for the modular curves X(N) and the Fermat curves with prime exponent.

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Cited by in corpus (3)

• Polynomial bounds for Arakelov invariants of Belyi curves
• On the arithmetic self-intersection numbers of the dualizing sheaf for Fermat curves of prime exponent
• Bounds for canonical Green's function at cusps