Dynamics of the Krichever construction in several variables

Abstract

The Krichever construction in one variable, that is, for spectral curves, linearizes the KdV-hierarchy on the jacobian of the curve. We carry out an appropriate generalization of the Krichever construction for an arbitrary projective variety $X$ and determine the corresponding nonlinear dynamics, which are then linearized on an extension of $Pic^0(X)$.