Let $X$ be a smooth Fano threefold over an algebraically closed field of positive characteristic. Assume that both the index and the Picard number are equal to one. We prove that $3 \leq g \leq 12$ for the genus $g$ of $X$. Moreover, we show that there exists no smooth curve on $X$ along which the blowup is Fano.PDF: Fano threefolds in positive characteristic II.pdf
