  The hypersurface in a 3-dimensional vector space with an isolated
quasi-homogeneous elliptic singularity of type E_r,r=6,7,8, has a natural
Poisson structure. We show that the family of del Pezzo surfaces of the
corresponding type E_r provides a semiuniversal Poisson deformation of that
Poisson structure.
  We also construct a deformation-quantization of the coordinate ring of such a
del Pezzo surface. To this end, we first deform the polynomial algebra C[x,y,z]
to a noncommutative algebra with generators x,y,z and the following 3 relations
(where [u,v]_t = uv- t.vu):
  [x,y]_t=F_1(z),
  [y,z]_t=F_2(x),
  [z,x]_t=F_3(y).
  This gives a family of Calabi-Yau algebras A(F) parametrized by a complex
number t and a triple F=(F_1,F_2,F_3), of polynomials in one variable of
specifically chosen degrees.
  Our quantization of the coordinate ring of a del Pezzo surface is provided by
noncommutative algebras of the form A(F)/(g) where (g) stands for the ideal of
A(F) generated by a central element g, which generates the center of the
algebra A(F) if F is generic enough.
