From Geometry of Jets to Quasiclassical Hierarchies

Abstract

I consider quasiclassical integrable systems, starting from the well-known dispersionless KdV and Toda hierarchies, which can be totally understood in terms of jet spaces over the rational curves with one or two punctures. For the nontrivial geometry of the higher genus curves, the same approach leads to construction of quasiclassical tau-functions or prepotentials, using the period integrals for Abelian differentials. I discuss also some physical applications of this construction.