Coisotropic deformations of algebraic varieties and integrable systems

Details Coisotropic deformations of algebraic varieties and integrable systems Coisotropic deformations of algebraic varieties and integrable systems

2009-06-18

arxiv.org/abs/0906.3399v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

17 pages, no figures

Scientific paper

Coisotropic deformations of algebraic varieties are defined as those for which an ideal of the deformed variety is a Poisson ideal. It is shown that coisotropic deformations of sets of intersection points of plane quadrics, cubics and space algebraic curves are governed, in particular, by the dKP, WDVV, dVN, d2DTL equations and other integrable hydrodynamical type systems. Particular attention is paid to the study of two- and three-dimensional deformations of elliptic curves. Problem of an appropriate choice of Poisson structure is discussed.

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