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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



On arithmetic intersection numbers on self-products of curves

Author: Robert Wilms
Journal: J. Algebraic Geom. 31 (2022), 397-424
Published electronically: January 4, 2022
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Abstract | References | Additional Information

Abstract: We give a closed formula for the Néron–Tate height of tautological integral cycles on Jacobians of curves over number fields as well as a new lower bound for the arithmetic self-intersection number $\hat {\omega }^2$ of the dualizing sheaf of a curve in terms of Zhang’s invariant $\varphi$. As an application, we obtain an effective Bogomolov-type result for the tautological cycles. We deduce these results from a more general combinatorial computation of arithmetic intersection numbers of adelic line bundles on higher self-products of curves, which are linear combinations of pullbacks of line bundles on the curve and the diagonal bundle.

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Additional Information

Robert Wilms
Affiliation: Department of Mathematics and Computer Science, University of Basel, Spiegelgasse 1, 4051 Basel, Switzerland
MR Author ID: 975037

Received by editor(s): February 20, 2020
Received by editor(s) in revised form: August 27, 2020
Published electronically: January 4, 2022
Additional Notes: The author was supported by SFB/Transregio 45.
Article copyright: © Copyright 2022 University Press, Inc.