## Nagoya Mathematical Journal

### Normal functions and the height of Gross–Schoen cycles

Robin de Jong

#### 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.

#### Article information

Source
Nagoya Math. J., Volume 214 (2014), 53-77.

Dates
First available in Project Euclid: 15 January 2014

https://projecteuclid.org/euclid.nmj/1389795890

Digital Object Identifier
doi:10.1215/00277630-2413391

Mathematical Reviews number (MathSciNet)
MR3211818

Zentralblatt MATH identifier
1312.14073

#### Citation

de Jong, Robin. Normal functions and the height of Gross–Schoen cycles. Nagoya Math. J. 214 (2014), 53--77. doi:10.1215/00277630-2413391. https://projecteuclid.org/euclid.nmj/1389795890

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