We investigate the concept of projectively equivariant quantization in the
framework of super projective geometry. When the projective superalgebra
pgl(p+1|q) is simple, our result is similar to the classical one in the purely
even case: we prove the existence and uniqueness of the quantization except in
some critical situations. When the projective superalgebra is not simple (i.e.
in the case of pgl(n|n)\not\cong sl(n|n)), we show the existence of a
one-parameter family of equivariant quantizations. We also provide explicit
formulas in terms of a generalized divergence operator acting on supersymmetric
tensor fields.Comment: 19 page
