Differential equations associated to Families of Algebraic Cycles

Details Differential equations associated to Families of Algebraic Cycles Differential equations associated to Families of Algebraic Cycles

2003-05-20

arxiv.org/abs/math/0305288v7

Mathematics

Algebraic Geometry

8 pages. Final version. To be published in Annales de l'Institute Fourier

Scientific paper

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.

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