Differential equations associated to Families of Algebraic Cycles

Abstract

We develop a theory of differential equations associated to families of algebraic cycles in higher Chow groups (i.e., motivic cohomology groups). This formalism is related to inhomogeneous Picard--Fuchs type differential equations. For families of K3 surfaces the corresponding non-linear ODE turns out to be symilar to Chazy's equation.Comment: 8 pages. Final version. To be published in Annales de l'Institute Fourie