Restricted volumes on K\"ahler manifolds
Complex Variables
2022-07-12 v2 Algebraic Geometry
Differential Geometry
Abstract
We study numerical restricted volumes of (1,1) classes on compact Kahler manifolds, as introduced by Boucksom. Inspired by work of Ein-Lazarsfeld-Mustata-Nakamaye-Popa on restricted volumes of line bundles on projective manifolds, we pose a natural conjecture to the effect that irreducible components of the non-Kahler locus of a big class should have vanishing numerical restricted volume. We prove this conjecture when the class has a Zariski decomposition, and give several applications.
Keywords
Cite
@article{arxiv.1608.07089,
title = {Restricted volumes on K\"ahler manifolds},
author = {Tristan C. Collins and Valentino Tosatti},
journal= {arXiv preprint arXiv:1608.07089},
year = {2022}
}
Comments
30 pages, improved exposition, final version to appear in les Annales de la Faculte des Sciences de Toulouse