On the anti-canonical geometry of weak $\mathbb{Q}$-Fano threefolds, III

Abstract

For a terminal weak $\mathbb{Q}$-Fano $3$-fold $X$, we show that the $m$-th anti-canonical map defined by $|-m{K}_X|$ is birational for all $m\ge 59$.

26 pages, to appear in Nagoya Math. J.; minor corrections applied

References in corpus (2)

• An effective upper bound for anti-canonical volumes of canonical $\mathbb{Q}$-Fano threefolds
• Characterizing terminal Fano threefolds with the smallest anti-canonical volume