## Kyoto Journal of Mathematics

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

Takayuki Koike

#### Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1441824039

Digital Object Identifier
doi:10.1215/21562261-3089091

Mathematical Reviews number (MathSciNet)
MR3395981

Zentralblatt MATH identifier
1323.32011

#### Citation

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. https://projecteuclid.org/euclid.kjm/1441824039

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