On numerically trivial automorphisms of threefolds of general type

Abstract

In this paper, we prove that the group ${\mathrm{Aut}}_{\mathbb{Q}}(X)$ of numerically trivial automorphisms are uniformly bounded for smooth projective threefolds $X$ of general type which either satisfy $q(X)\ge 3$ or have a Gorenstein minimal model. If $X$ is furthermore of maximal Albanese dimension, then $|{\mathrm{Aut}}_{\mathbb{Q}}(X)|\le 4$, and 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.

21 pages; minor changes according to the referee report; to appear in Mathematical Research Letters

References in corpus (2)

• Some results on the eventual paracanonical maps
• On topologically trivial automorphisms of compact Kähler manifolds and algebraic surfaces