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arXiv · 1304.1289

Minimal singular metrics of a line bundle admitting no Zariski-decomposition

Takayuki Koike
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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.

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Takayuki Koike. 2013-04-04. Minimal singular metrics of a line bundle admitting no Zariski-decomposition. https://arxiv.org/abs/1304.1289

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