  We prove that several Feigin-Odesskii Poisson brackets associated with normal
elliptic curves in ${\mathbb P}^n$ are compatible if and only if they are
contained in a scroll or in a Veronese surface in ${\mathbb P}^5$ (with an
exception of one case when $n=3$). In the case $n=3$ we determine the quartic
corresponding to the Schouten bracket of two (non-compatible) Poisson brackets
associated with normal elliptic curves $E_1$ and $E_2$.
