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arXiv · 1702.03514

Adelic Cartier divisors with base conditions and the continuity of volumes

Hideaki Ikoma
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Abstract

In the previous paper [7], we introduced a notion of pairs of adelic R-Cartier divisors and R-base conditions. The purpose of this paper is to propose an extended notion of adelic R-Cartier divisors that we call an l1-adelic R-Cartier divisors, and to show that the arithmetic volume function defined on the space of pairs of l1-adelic R-Cartier divisors and R-base conditions is continuous along the directions of l1-adelic R-Cartier divisors.

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Hideaki Ikoma. 2017-02-12. Adelic Cartier divisors with base conditions and the continuity of volumes. https://doi.org/10.1215/21562261-2021-0018

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