I am looking for the preprint
A. Bondal, Noncommutative deformations and Poisson brackets on projective spaces. Preprint MPI/93-67
which I could not find online. Does anyone have an eletronic version of it ?
I am interested in the conjecture made there which predicts that the locus where the rank of a holomorphic Poisson bracket on a Fano manifold is smaller than $k$ has dimension strictly greater than $k$, see for instance Section 2 of Beauville's problem list in holomorphic symplectic geometry. Some progress has been made by Polishchuck in Algebraic Geometry of Poisson Brackets (Journal of Mathematical Sciences 84 no. 5, 1997); and by Druel in Structures de Poisson sur les variétés algébriques de dimension 3 (Bull. Soc. Mat. France 127, 1999).
Any further references on this conjecture will be welcome.