Postulation of general quartuple fat point schemes in P^3
  We study the postulation of a general union $Y$ of double, triple, and quartuple points of $\mathbb{P}^3$. We prove that $Y$ has the expected postulation in degree $d\ge 41$, using the Horace differential lemma. We also discuss the cases of low degree with the aid of computer algebra. 
Edoardo Ballico and Maria Chiara Brambilla