Tohoku Mathematical Journal
2015
June
SECOND SERIES VOL. 67, NO. 2

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

Title MINIMAL SINGULAR METRICS OF A LINE BUNDLE ADMITTING NO ZARISKI DECOMPOSITION

Author Takayuki Koike

(Received October 11, 2013, revised April 17, 2014)
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.

Mathematics Subject Classification. Primary 32J25; Secondary 32J27, 14C20.
Key words and phrases. Minimal singular metrics, Zariski decompositions, Nakayama example, Kiselman numbers, Lelong numbers, non-nef loci, multiplier ideal sheaves.

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