MINIMAL SINGULAR METRICS OF A LINE BUNDLE ADMITTING NO ZARISKI DECOMPOSITION

TAKAYUKI KOIKE

doi:10.2748/tmj/1435237045

Tohoku Mathematical Journal, Second Series

Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735

MINIMAL SINGULAR METRICS OF A LINE BUNDLE ADMITTING NO ZARISKI DECOMPOSITION

TAKAYUKI KOIKE

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Keywords: Minimal singular metrics, Zariski decompositions, Nakayama example, Kiselman numbers, Lelong numbers, non-nef loci, multiplier ideal sheaves

JOURNAL FREE ACCESS

2015 Volume 67 Issue 2 Pages 297-321

DOI https://doi.org/10.2748/tmj/1435237045

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Abstract

We give a concrete expression of a minimal singular metric on 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 modifications. As an application, we discuss the Zariski closedness of non-nef loci.

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