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

2009/06/11 by Ulf Kuehn, Kuehn, Ulf
Mathematics · #11G18 #11G30 #14G40 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11G18 #msc:11G30 #msc:14G40

paper · pdf · doi:10.48550/arxiv.0906.2056

slightly changed version

openalex publication_date 2009/06/11 · arxiv created 2013/08/14 · arxiv updated 2013/08/15 · openalex created_date 2022/08/28 · openalex updated_date 2026/07/28

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

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• Lower bounds on the arithmetic self-intersection number of the relative dualizing sheaf on arithmetic surfaces
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• Self-intersection of dualizing sheaves of arithmetic surfaces with reducible fibers
• Numerical cohomology for arithmetic surfaces and applications