  Within the framework of deformation quantization, a first step towards the
study of star-products is the calculation of Hochschild cohomology. The aim of
this article is precisely to determine the Hochschild homology and cohomology
in two cases of algebraic varieties. On the one hand, we consider singular
curves of the plane; here we recover, in a different way, a result proved by
Fronsdal and make it more precise. On the other hand, we are interested in
Klein surfaces. The use of a complex suggested by Kontsevich and the help of
Groebner bases allow us to solve the problem.
