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arXiv · 1201.2216

Effective bound of linear series on arithmetic surfaces

Xinyi Yuan·Tong Zhang
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Abstract

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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Xinyi Yuan, Tong Zhang. 2012-01-11. Effective bound of linear series on arithmetic surfaces. https://doi.org/10.1215/00127094-2322779

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