On minimal 3-folds of general type with maximal pluricanonical section index

Abstract

Let $X$ be a minimal projective 3-fold of general type. The pluricanonical section index $δ(X)$ is defined to be the minimal integer $m$ so that $P_{m}(X)\geq 2$. According to Chen-Chen, one has either $1\leq δ(X)\leq 15$ or $δ(X)=18$. This note aims to intensively study those with maximal such index. A direct corollary is that the $57$th canonical map of every minimal 3-fold of general type is stably birational.

To appear in The Asian Journal of Mathematics (Special issue for Ngaiming Mok's sixtieth birthday)