Differential equations associated to Families of Algebraic Cycles

2003/05/20 by del Angel, Pedro Luis, Müller-Stach, Stefan · 1 citation
#14C25 (Primary) #19E20 (Secondary) #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.math/0305288

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.

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• Construction of Higher Chow cycles on cyclic coverings of ℙ¹ × ℙ¹

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