Kyoto Journal of Mathematics

Big arithmetic divisors on the projective spaces over Z

Atsushi Moriwaki

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In this paper, we observe several properties of an arithmetic divisor D¯ on PZn and give the exact form of the Zariski decomposition of D¯ on PZ1. Further, we show that, if n2 and D¯ is big and non-nef, then for any birational morphism f:XPZn of projective, generically smooth, and normal arithmetic varieties, we cannot expect a suitable Zariski decomposition of f(D¯). We also give a concrete construction of Fujita’s approximation of D¯.

Article information

Kyoto J. Math., Volume 51, Number 3 (2011), 503-534.

First available in Project Euclid: 1 August 2011

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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]


Moriwaki, Atsushi. Big arithmetic divisors on the projective spaces over $\mathbb{Z}$. Kyoto J. Math. 51 (2011), no. 3, 503--534. doi:10.1215/21562261-1299882.

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