Self-intersection of dualizing sheaves of arithmetic surfaces with reducible fibers

1995/02/16 by Atsushi Moriwaki, Moriwaki, Atsushi
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9502014

8 pages, AmS-TeX

arxiv created 1995/02/16 · arxiv updated 2009/11/30

Abstract

Let K be an algebraic number field and O_K the ring of integers of K. Let f : X --> Spec(O_K) be a stable arithmetic surface over O_K of genus g >= 2. In this short note, we will prove that if f has a reducible geometric fiber, then the self intersection of dualizing sheaf of X with Arakelov metric is greater than or equal to log(2)/6(g-1).

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