Irreducibility of the set of cubic polynomials with one periodic   critical point
  The space of monic centered cubic polynomials with marked critical points is isomorphic to C^2. For each n>0, the locus Sn formed by all polynomials with a specified critical point periodic of exact period n forms an affine algebraic set. We prove that Sn is irreducible, thus giving an affirmative answer to a question posed by Milnor. (This manuscript has been withdrawn) 
Matthieu Arfeux and Jan Kiwi
math.DS