  We examine the Hochschild cohomology governing graded deformations for finite
cyclic groups acting on polynomial rings. We classify the infinitesimal graded
deformations of the skew group algebra $S\rtimes G$ for a cyclic group $G$
acting on a polynomial ring $S$. This gives all graded deformations of the
first order. We are particularly interested in the case when the characteristic
of the underlying field divides the order of the acting group, which
complicates the determination of cohomology.
