Estimation of arithmetic linear series

Abstract

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

34 pages

References in corpus (2)

• On Volumes of Arithmetic Line Bundles
• Positive degree and arithmetic bigness

Cited by in corpus (10)

• Toward Dirichlet's unit theorem on arithmetic varieties
• Big arithmetic divisors on the projective spaces over Z
• Effective bound of linear series on arithmetic surfaces
• Zariski decompositions on arithmetic surfaces
• Volumes of Arithmetic Okounkov Bodies
• Remarks on the arithmetic restricted volumes and the arithmetic base loci
• Effective Bounds of Linear Series on Algebraic Varieties and Arithmetic Varieties
• Free basis consisting of strictly small sections
• Arithmetic linear series with base conditions
• Differentiability of the arithmetic volume function along the base conditions