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Abstract: Lazarsfeld and Mustata propose general and systematic usage of Okounkov-sidea in order to study asymptotic behavior of linear series on an algebraicvariety. It is a very simple way, but it yields a lot of consequences, likeFujita-s approximation theorem. Yuan generalized this way to the arithmeticsituation, and he established the arithmetic Fujita-s approximation theorem,which was also proved by Chen independently. In this paper, we introducearithmetic linear series and give a general way to estimate them based onYuan-s idea. As an application, we consider an arithmetic analogue of thealgebraic restricted volumes.

Autor: Atsushi Moriwaki


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