Arkiv för Matematik

  • Ark. Mat.
  • Volume 55, Number 1 (2017), 131-153.

Approximations and examples of singular Hermitian metrics on vector bundles

Genki Hosono

Full-text: Open access

Abstract

We study singular Hermitian metrics on vector bundles. There are two main results in this paper. The first one is on the coherence of the higher rank analogue of multiplier ideals for singular Hermitian metrics defined by global sections. As an application, we show the coherence of the multiplier ideal of some positively curved singular Hermitian metrics whose standard approximations are not Nakano semipositive. The aim of the second main result is to determine all negatively curved singular Hermitian metrics on certain type of vector bundles, for example, certain rank $2$ bundles on elliptic curves.

Article information

Source
Ark. Mat., Volume 55, Number 1 (2017), 131-153.

Dates
Received: 15 November 2015
Revised: 9 December 2016
First available in Project Euclid: 2 February 2018

Permanent link to this document
https://projecteuclid.org/euclid.afm/1517535605

Digital Object Identifier
doi:10.4310/ARKIV.2017.v55.n1.a6

Mathematical Reviews number (MathSciNet)
MR3711145

Zentralblatt MATH identifier
06823276

Subjects
Primary: 32L10: Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F05, 18F20, 55N30]
Secondary: 14F18: Multiplier ideals

Keywords
singular Hermitian metric vector bundles multiplier ideal sheaves

Citation

Hosono, Genki. Approximations and examples of singular Hermitian metrics on vector bundles. Ark. Mat. 55 (2017), no. 1, 131--153. doi:10.4310/ARKIV.2017.v55.n1.a6. https://projecteuclid.org/euclid.afm/1517535605


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