  We study nonanticommutative deformations of N=2 two-dimensional Euclidean
sigma models. We find that these theories are described by simple deformations
of Zumino's Lagrangian and the holomorphic superpotential. Geometrically, this
deformation can be interpreted as a fuzziness in target space controlled by the
vacuum expectation value of the auxiliary field. In the case of
nonanticommutative deformations preserving Euclidean invariance, we find that a
continuation of the deformed supersymmetry algebra to Lorentzian signature
leads to a rather intriguing central extension of the ordinary (2,2)
superalgebra.
