Néron-Tate heights of cycles on jacobians

Abstract

We develop a method to calculate the Néron-Tate height of tautological integral cycles on jacobians of curves defined over number fields. As examples we obtain closed expressions for the Néron-Tate height of the difference surface, the Abel-Jacobi images of the square of the curve, and of any symmetric theta divisor. As applications we obtain a new effective positive lower bound for the essential minimum of any Abel-Jacobi image of the curve and a proof, in the case of jacobians, of a formula proposed by Autissier relating the Faltings height of a principally polarized abelian variety with the Néron-Tate height of a symmetric theta divisor.

35 pages, SAGE file written by David Holmes is available as an ancillary file, v2: minor revisions

References in corpus (2)

• New explicit formulas for Faltings' delta-invariant
• Canonical 2-forms on the moduli space of Riemann surfaces

Cited by in corpus (6)

• On arithmetic intersection numbers on self-products of curves
• Vanishing results in Chow groups for the modified diagonal cycles
• Faltings height and Néron-Tate height of a theta divisor
• Heights on square of modular curves
• On the height of Gross-Schoen cycles in genus three
• A uniform quantitative Manin-Mumford theorem for curves over function fields