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arXiv · alg-geom/9502014

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

Atsushi Moriwaki
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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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BibTeXRIS

Atsushi Moriwaki. 1995-02-16. Self-intersection of dualizing sheaves of arithmetic surfaces with reducible fibers. https://arxiv.org/abs/alg-geom/9502014

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