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Normal functions and the height of Gross-Schoen cycles

Published online by Cambridge University Press:  11 January 2016

Robin De Jong
Robin De Jong*
Affiliation:
Mathematical Institute University of Leiden2300 RA Leiden TheNetherlandsrdejong@math.leidenuniv.nl
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Abstract

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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.

Keywords

14G4014C2514D06
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 214 , June 2014 , pp. 53 - 77
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2014

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