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

Ulf Kuehn

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arXiv · 0906.2056

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

Ulf Kuehn

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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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Ulf Kuehn. 2009-06-11. On the arithmetic self-intersection number of the dualizing sheaf on arithmetic surfaces. https://arxiv.org/abs/0906.2056

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