Geometric differential equations on bundles of Jacobians of curves of genus 1 and 2

Abstract

. We construct some differential equations describing the geometry of bundles of Jacobians of algebraic curves of genus 1 and 2. For an elliptic curve we produce differential equations on the coefficients of a cometric compatible with the Gauss–Manin connection of the universal bundle of Jacobians of elliptic curves. This cometric is defined in terms of a solution F of the linear system of differential equations