2024/09/30 by Chen, Jingshan, Wang, Chongning, Zhang, Lei · 1 citation
#14D99 #14G17 #14J10 #14J32 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2409.19973
In this paper, we classify irregular threefolds with numerically trivial canonical divisors in positive characteristic. For such a variety, if its Albanese dimension is not maximal, then the Albanese morphism will induce a fibration which either maps to a curve or is fibered by curves. In practice, we treat arbitrary dimensional irregular varieties with either one dimensional Albanese fiber or one dimensional Albanese image. We prove that such a variety carries another fibration transversal to its Albanese morphism (a "bi-fibration" structure), which is an analog structure of bielliptic or quasi-bielliptic surfaces. In turn, we give an explicit description of irregular threefolds with trivial canonical divisors.