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Differential approach for the study of duals of algebraic-geometric codes on surfaces

Alain Couvreur (2011)

Journal de Théorie des Nombres de Bordeaux

The purpose of the present article is the study of duals of functional codes on algebraic surfaces. We give a direct geometrical description of them, using differentials. Even if this description is less trivial, it can be regarded as a natural extension to surfaces of the result asserting that the dual of a functional code C L ( D , G ) on a curve is the differential code C Ω ( D , G ) . We study the parameters of such codes and state a lower bound for their minimum distance. Using this bound, one can study some examples...

Differential Equations associated to Families of Algebraic Cycles

Pedro Luis del Angel, Stefan Müller-Stach (2008)

Annales de l’institut Fourier

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 inhomogenous Picard–Fuchs type differential equations. For a families of K3 surfaces the corresponding non–linear ODE turns out to be similar to Chazy’s equation.

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