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June 2014 Normal functions and the height of Gross–Schoen cycles
Robin de Jong
Nagoya Math. J. 214: 53-77 (June 2014). DOI: 10.1215/00277630-2413391

Abstract

We prove a variant of a formula due to Zhang relating the Beilinson–Bloch height of the Gross–Schoen cycle on a pointed curve with the self-intersection of its relative dualizing sheaf. In our approach, the height of the Gross–Schoen cycle occurs as the degree of a suitable Bloch line bundle. We show that the Chern form of this line bundle is nonnegative, and we calculate its class in the Picard group of the moduli space of pointed stable curves of compact type. The basic tools are normal functions and biextensions associated to the cohomology of the universal Jacobian.

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Robin de Jong. "Normal functions and the height of Gross–Schoen cycles." Nagoya Math. J. 214 53 - 77, June 2014. https://doi.org/10.1215/00277630-2413391

Information

Published: June 2014
First available in Project Euclid: 15 January 2014

zbMATH: 1312.14073
MathSciNet: MR3211818
Digital Object Identifier: 10.1215/00277630-2413391

Subjects:
Primary: 14G40
Secondary: 14C25 , 14D06

Rights: Copyright © 2014 Editorial Board, Nagoya Mathematical Journal

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Vol.214 • June 2014
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