Duke Mathematical Journal

Effective bound of linear series on arithmetic surfaces

Xinyi Yuan and Tong Zhang

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We prove effective upper bounds 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.

Article information

Duke Math. J., Volume 162, Number 10 (2013), 1723-1770.

First available in Project Euclid: 11 July 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14G40: Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30]
Secondary: 11G50: Heights [See also 14G40, 37P30]


Yuan, Xinyi; Zhang, Tong. Effective bound of linear series on arithmetic surfaces. Duke Math. J. 162 (2013), no. 10, 1723--1770. doi:10.1215/00127094-2322779. https://projecteuclid.org/euclid.dmj/1373546603

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