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

2013/04/04 by Takayuki Koike, Koike, Takayuki
Mathematics · #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1304.1289

Abstract

We give a concrete expression of a minimal singular metric of a big line bundle on a compact Kähler 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 Kollár in this class.

Citations

• On the extension ofL 2 holomorphic functions

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