Michigan Mathematical Journal

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

Michiel Jespers and Robin de Jong

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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.

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Michigan Math. J., Volume 69, Issue 1 (2020), 3-40.

Received: 16 October 2017
Revised: 25 May 2018
First available in Project Euclid: 2 August 2019

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Zentralblatt MATH identifier

Primary: 14D05: Structure of families (Picard-Lefschetz, monodromy, etc.) 14D06: Fibrations, degenerations 14E05: Rational and birational maps 14G40: Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30] 32C30: Integration on analytic sets and spaces, currents {For local theory, see 32A25 or 32A27}


Jespers, Michiel; de Jong, Robin. Chern–Weil Theory for Line Bundles with the Family Arakelov Metric. Michigan Math. J. 69 (2020), no. 1, 3--40. doi:10.1307/mmj/1564711314. https://projecteuclid.org/euclid.mmj/1564711314

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