2019/06/27 by Hang Zhao, Zhao, Hang
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG
paper · pdf · doi:10.48550/arxiv.1906.11469
openalex publication_date 2019/06/27 · arxiv created 2022/06/09 · arxiv updated 2022/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a minimal projective threefold of general type over ℂ with only Gorenstein quotient singularities, and let Autℚ(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 |Autℚ(X)|≤ 6. Moreover, if X is nonsingular and KX is ample, then |Autℚ(X)|≤ 5. Seeking for higher-dimensional examples of varieties with nontrivial Autℚ(X), we concern d-folds X isogenous to an unmixed product of curves. If d=3, we show that Autℚ(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 Autℚ(X) being trivial. Curiously, there exist examples of projective threefolds X with terminal singularities and maximal Albanese dimension whose Autℚ(X) can have an arbitrarily large order.