Question

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.

Answer 1

Preprint of Bondal can be found here:

http://www.mi.ras.ru/~akuznet/math/Bondal%20Non-commutative%20deformations%20and%20Poisson%20brackets%20on%20projective%20spaces.pdf

Another related reference is the following paper

Fano threefolds with sections in $Ω^1(1)$, by Priska Jahnke and Ivo Radloff.