Bertini's theorem for $F$-rational $F$-pure singularities

Alessandro De Stefani, Thomas Polstra, Austyn Simpson

Let $k$ be an algebraically closed field of characteristic $p>0$, and let $X\subseteq {\mathbb{P}}_k^n$ be a quasi-projective variety that is $F$-rational and $F$-pure. We prove that…