Effective bound of linear series on arithmetic surfaces

Details Effective bound of linear series on arithmetic surfaces Effective bound of linear series on arithmetic surfaces

2012-01-11

arxiv.org/abs/1201.2216v2

Mathematics

Number Theory

Scientific paper

We prove an effective upper bound on the number of effective sections of a hermitian line bundle over an arithmetic surface. It is an effective version of the arithmetic Hilbert--Samuel formula in the nef case. As a consequence, we obtain effective lower bounds on the Faltings height and on the self-intersection of the canonical bundle in terms of the number of singular points on fibers of the arithmetic surface.

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