Automorphisms of threefolds of general type acting trivially in cohomology.

Let X be a minimal projective threefold of general type over C with only Gorenstein quotient singularities, and let Aut Q (X) be the subgroup of automorphisms acting trivially on H ∗ (X , Q) . In this paper, we show that if X is of maximal Albanese dimension, then | Aut Q (X) | ≤ 6 . Moreover, if X is nonsingular and K X is ample, then | Aut Q (X) | ≤ 5 . Seeking for higher-dimensional examples of varieties with nontrivial Aut Q (X) , we concern d-folds X isogenous to an unmixed product of curves. If d = 3 , we show that Aut Q (X) is a 2-elementray abelian group whose order is at most 4 under some conditions on their minimal realizations. Moreover, each of the possible groups can be realized. If d ≥ 3 , we give a sufficient condition for Aut Q (X) being trivial. Curiously, there exist examples of projective threefolds X with terminal singularities and maximal Albanese dimension whose Aut Q (X) can have an arbitrarily large order. [ABSTRACT FROM AUTHOR]