Tohoku Mathematical Journal

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 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

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

Dates
First available in Project Euclid: 25 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1435237045

Digital Object Identifier
doi:10.2748/tmj/1435237045

Mathematical Reviews number (MathSciNet)
MR3365374

Zentralblatt MATH identifier
1326.32031

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

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

Citation

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. https://projecteuclid.org/euclid.tmj/1435237045


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