Numerical characterization of nef arithmetic divisors on arithmetic surfaces
Atsushi Moriwaki
TL;DR
This paper provides a numerical criterion to identify nef arithmetic divisors on arithmetic surfaces, linking nefness to pseudo-effectiveness and a specific degree-volume equality.
Contribution
It introduces a precise numerical characterization of nef arithmetic R-Cartier divisors on arithmetic surfaces, connecting geometric properties with numerical invariants.
Findings
Nef divisors are characterized by pseudo-effectiveness and deg(D^2) = vol(D)
Provides a practical criterion for nefness on arithmetic surfaces
Bridges geometric and numerical aspects of arithmetic divisors
Abstract
In this paper, we give a numerical characterization of nef arithmetic R-Cartier divisors of C^0-type on an arithmetic surface. Namely an arithmetic R-Cartier divisor D of C^0-type is nef if and only if D is pseudo-effective and deg(D^2) = vol(D).
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Meromorphic and Entire Functions · Advanced Differential Equations and Dynamical Systems