Tohoku Mathematical Journal

Minimal singular metrics of a line bundle admitting no Zariski decomposition

Takayuki Koike

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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.

Article information

Tohoku Math. J. (2), Volume 67, Number 2 (2015), 297-321.

First available in Project Euclid: 25 June 2015

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Zentralblatt MATH identifier

Primary: 32J25: Transcendental methods of algebraic geometry [See also 14C30]
Secondary: 32J27: Compact Kähler manifolds: generalizations, classification 14C20: Divisors, linear systems, invertible sheaves

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


Koike, Takayuki. Minimal singular metrics of a line bundle admitting no Zariski decomposition. Tohoku Math. J. (2) 67 (2015), no. 2, 297--321. doi:10.2748/tmj/1435237045.

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