On the topology of projective subspaces in complex Fermat varieties
  Let X be the complex Fermat variety of dimension n=2d and degree m>2. We investigate the submodule of the middle homology group of X with integer coefficients generated by the classes of standard d-dimensional subspaces contained in X, and give an algebraic (or rather combinatorial) criterion for the primitivity of this submodule. 
Alex Degtyarev and Ichiro Shimada
math.AG