We are interested in equivariant embeddings of homogeneous spaces. Given the standard action
of C^2 on itself, we look for complex surfaces M acted upon by C^2 so as M should include an
invariant copy of C^2 where the restriction of the (extended) action recovers C^2
acting on itself. In particular, for a given equivariant C^2-embedding,  we shall provide a local classification of the action  by means of a description of the corresponding local transformation group.

This is joint work with Julio Rebelo, Helena Reis and Ana Cristina Ferreira.