The Hilali Conjecture for hyperelliptic spaces
  The Hilali Conjecture predicts that for a simply-connected elliptic space, the total dimension of the rational homotopy does not exceed that of the rational homology. Here we give a proof of this conjecture for a class of elliptic spaces known as hyperelliptic. 
Javier Fernandez de Bobadilla, Javier Fresan, Vicente Mu\~noz, and   Aniceto Murillo
math.AT