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

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 con...

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Bibliographic Details
Published in:arXiv.org 2013-08
Main Author: Kuehn, Ulf
Format: Article
Language:English
Subjects:
Arithmetic
Subgroups
Upper bounds
Online Access:Get full text
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Summary: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.
ISSN:2331-8422