On the height of Gross-Schoen cycles in genus three

Abstract

We show that there exists a sequence of genus three curves defined over the rationals in which the height of a canonical Gross-Schoen cycle tends to infinity.

26 pages; v2: referee's remarks taken into account

References in corpus (5)

• Johnson's homomorphisms and the Arakelov-Green function
• Néron-Tate heights of cycles on jacobians
• SL_2-orbits and degenerations of mixed Hodge structure
• Positivity of the height jump divisor
• Positivity of heights of codimension 2 cycles over function field of characteristic 0