Rational linear subspaces of hypersurfaces over finite fields

María Inés de Frutos Fernández, Sumita Garai, Kelly Isham +2

Let $X\subset {\mathbb{P}}^n$ be a hypersurface of degree $d$ defined over a finite field of characteristic $p>0$. We prove that if $n\ge r+\left(\genfrac{}{}{0ex}{}{d+r}{r+1}\right)$, then $X$ contains…