Vacuum curves and classical integrable systems in $2+1$ discrete dimensions

A dynamical system in discrete time is studied by means of algebraic geometry. This system has reductions which can be interpreted as classical field theory in the $2+1$ discrete space-time. The study is based on the technique of vacuum curves and vacuum vectors. The evolution of the system has hyperbolic character, i.e., has a finite propagation speed. Bibl. 10 titles.