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

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

1995-02-16

arxiv.org/abs/alg-geom/9502014v1

Mathematics

Algebraic Geometry

8 pages, AmS-TeX

Scientific paper

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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