Coisotropic deformations of algebraic varieties and integrable systems

Abstract

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.

17 pages, no figures

References in corpus (6)

• Coisotropic deformations of associative algebras and dispersionless integrable hierarchies
• Singular sector of the Burgers-Hopf hierarchy and deformations of hyperelliptic curves
• Integrable Quasiclassical Deformations of Algebraic Curves
• Dispersionless integrable equations as coisotropic deformations. Extensions and reductions
• Quasiclassical generalized Weierstrass representation and dispersionless DS equation
• Integrable Quasiclassical Deformations of Cubic Curves

Cited by in corpus (4)

• Oriented Associativity Equations and Symmetry Consistent Conjugate Curvilinear Coordinate Nets
• Projective differential geometry of multidimensional dispersionless integrable hierarchies
• Cohomological, Poisson structures and integrable hierarchies in tautological subbundles for Birkhoff strata of Sato Grassmannian
• Hamiltonian motions of plane curves and formation of singularities and bubbles