Approximations and examples of singular Hermitian metrics on vector bundles

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.

Keywords

singular Hermitian metric, vector bundles, multiplier ideal sheaves

2010 Mathematics Subject Classification

Primary 32L10. Secondary 14F18.

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Received 15 November 2015

Received revised 9 December 2016

Accepted 21 December 2016

Published 26 September 2017