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We prove a variant of a formula due to S. Zhang relating the Beilinson-Blochheight of the Gross-Schoen cycle on a pointed curve with the self-intersectionof its relative dualizing sheaf. In our approach the height of the Gross-Schoencycle occurs as the degree of a suitable Bloch line bundle. We show that theChern form of this line bundle is non-negative, and we calculate its class inthe Picard group of the moduli space of pointed stable curves of compact type.The basic tools are normal functions and biextensions associated to thecohomology of the universal jacobian.

Normal functions and the height of Gross-Schoen cycles