On the topology of projective subspaces in complex Fermat varieties

Abstract

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.