Andriy Panasyuk
The Local Structure of some Complex Poisson Brackets
Preprint series: ESI preprints

MSC:

32B05 Analytic algebras and generalizations, preparation theorems

58F05 Hamiltonian and Lagrangian systems; symplectic geometry, See also {70Hxx, 81S10}

Abstract: We consider structures of complex Poisson brackets on the space
of $\C$-functions on complex $2n$-dimensional
manifold generated by $\d$-closed
non-degenerate $(2,0)$-form (with non-holomorphic coefficients). Is the
Darboux
theorem valid for such structures? We show that
the local structure of brackets depends on equivalence
class of corresponding $(2,0)$-form under biholomorphic maps.

Keywords: complex Poisson bracket, Poisson algebra