Minimal singular metrics of a line bundle admitting no Zariski-decomposition
Algebraic Geometry
2014-06-05 v2 Complex Variables
Abstract
We give a concrete expression of a minimal singular metric of a big line bundle on a compact K\"ahler manifold which is the total space of a toric bundle over a complex torus. In this class of manifolds, Nakayama constructed examples which have line bundles admitting no Zariski-decomposition even after any proper modifications. As an application, we discuss the Zariski-closedness of non-nef loci and the openness conjecture of Demailly and Koll\'{a}r in this class.
Keywords
Cite
@article{arxiv.1304.1289,
title = {Minimal singular metrics of a line bundle admitting no Zariski-decomposition},
author = {Takayuki Koike},
journal= {arXiv preprint arXiv:1304.1289},
year = {2014}
}
Comments
Minor format edition, 26 pages, 4 figures