English

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