On numerically trivial automorphisms of threefolds of general type

Abstract

$\def\AutQx{\mathrm{Aut}_\mathbb{Q}(X)}$ In this paper, we prove that the group $\AutQx$ of numerically trivial automorphisms are uniformly bounded for smooth projective threefolds X of general type which either satisfy $q(X) \geq 3$ or have a Gorenstein minimal model. If X is furthermore of maximal Albanese dimension, then $\lvert \AutQx \rvert \leq 4$, and the equality can be achieved by an unbounded family of threefolds previously constructed by the third author. Along the way we prove a Noether type inequality for log canonical pairs of general type with the coefficients of the boundary divisor from a given subset $\mathcal{C} \subset (0, 1]$ such that $\mathcal{C} \cup \{1\}$ attains the minimum.