## The Michigan Mathematical Journal

### Chern–Weil Theory for Line Bundles with the Family Arakelov Metric

#### Abstract

We prove a result of Chern–Weil type for canonically metrized line bundles on one-parameter families of smooth complex curves. Our result generalizes a result due to J. I. Burgos Gil, J. Kramer, and U. Kühn that deals with a line bundle of Jacobi forms on the universal elliptic curve over the modular curve with full level structure, equipped with the Petersson metric. Our main tool, as in the work by Burgos Gil, Kramer, and Kühn, is the notion of a b-divisor.

#### Article information

Source
Michigan Math. J., Advance publication (2019), 38 pages.

Dates
Revised: 25 May 2018
First available in Project Euclid: 2 August 2019

https://projecteuclid.org/euclid.mmj/1564711314

Digital Object Identifier
doi:10.1307/mmj/1564711314

#### Citation

Jespers, Michiel; de Jong, Robin. Chern–Weil Theory for Line Bundles with the Family Arakelov Metric. Michigan Math. J., advance publication, 2 August 2019. doi:10.1307/mmj/1564711314. https://projecteuclid.org/euclid.mmj/1564711314

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