Intersection theory of nef b-divisor classes
Abstract
We prove that any nef b-divisor class on a projective variety defined over an algebraically closed field of characteristic 0 is a decreasing limit of nef Cartier classes. Building on this technical result, we construct an intersection theory of nef b-divisors, and prove several variants of the Hodge index theorem inspired by the work of Dinh and Sibony. We show that any big and basepoint free curve class is a power of a nef b-divisor, and relate this statement to Zariski decompositions of curves classes introduced by Lehmann and Xiao. Our construction allows us to relate various Banach spaces contained in the space of b-divisors which were defined in our previous work.5
Keywords
Cite
@article{arxiv.2007.04549,
title = {Intersection theory of nef b-divisor classes},
author = {Nguyen-Bac Dang and Charles Favre},
journal= {arXiv preprint arXiv:2007.04549},
year = {2021}
}
Comments
38 pages. New version: updated references. Our main theorem is now valid over any alg. closed field of char. 0. A section on movable classes was added, but the section on toric b-classes was removed to streamline the discussion