Zariski decompositions on arithmetic surfaces
Atsushi Moriwaki
TL;DR
This paper develops the theory of Zariski decompositions for arithmetic R-divisors on arithmetic surfaces, providing new insights into their properties and extending the general framework of arithmetic divisors on varieties.
Contribution
It introduces the Zariski decomposition for arithmetic R-divisors of continuous type and explores their fundamental properties on arithmetic surfaces.
Findings
Established Zariski decompositions for arithmetic R-divisors
Analyzed properties of these decompositions
Extended the theory to general arithmetic varieties
Abstract
In this paper, we establish the Zariski decompositions of arithmetic R-divisors of continuous type on arithmetic surfaces and investigate several properties. We also develop the general theory of arithmetic R-divisors on arithmetic varieties.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Meromorphic and Entire Functions