On arithmetic intersection numbers on self-products of curves

Abstract

We give a close 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 $\phi$. 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.

22 pages. Comments are welcome!

References in corpus (1)

• Néron-Tate heights of cycles on jacobians

Cited by in corpus (4)

• Degeneration of Riemann theta functions and of the Zhang-Kawazumi invariant with applications to a uniform Bogomolov conjecture
• Vanishing results in Chow groups for the modified diagonal cycles
• Arithmetic bigness and a uniform Bogomolov-type result
• A uniform quantitative Manin-Mumford theorem for curves over function fields