Kyoto Journal of Mathematics

On the minimality of canonically attached singular Hermitian metrics on certain nef line bundles

Takayuki Koike

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We apply Ueda theory to a study of singular Hermitian metrics of a (strictly) nef line bundle L. Especially we study minimal singular metrics of L, metrics of L with the mildest singularities among singular Hermitian metrics of L whose local weights are plurisubharmonic. In some situations, we determine a minimal singular metric of L. As an application, we give new examples of (strictly) nef line bundles which admit no smooth Hermitian metric with semipositive curvature.

Article information

Kyoto J. Math., Volume 55, Number 3 (2015), 607-616.

Received: 17 June 2014
Accepted: 8 July 2014
First available in Project Euclid: 9 September 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32J25: Transcendental methods of algebraic geometry [See also 14C30]
Secondary: 14C20: Divisors, linear systems, invertible sheaves

nef line bundles singular Hermitian metrics minimal singular metrics Ueda theory


Koike, Takayuki. On the minimality of canonically attached singular Hermitian metrics on certain nef line bundles. Kyoto J. Math. 55 (2015), no. 3, 607--616. doi:10.1215/21562261-3089091.

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