English

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

Number Theory 2013-08-15 v2 Algebraic Geometry

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 Γ0(N)\Gamma_0(N) with square free level, as well as for the modular curves X(N) and the Fermat curves with prime exponent.

Keywords

Cite

@article{arxiv.0906.2056,
  title  = {On the arithmetic self-intersection number of the dualizing sheaf on arithmetic surfaces},
  author = {Ulf Kuehn},
  journal= {arXiv preprint arXiv:0906.2056},
  year   = {2013}
}

Comments

slightly changed version

R2 v1 2026-06-21T13:12:14.243Z