Irregular threefolds with numerically trivial canonical divisor

TL;DR

This paper classifies irregular threefolds with numerically trivial canonical divisors in positive characteristic, revealing their fibration structures and providing explicit descriptions of such varieties.

Contribution

It introduces a new classification framework for irregular threefolds with trivial canonical divisors, highlighting bi-fibration structures analogous to bielliptic surfaces.

Findings

Existence of a bi-fibration structure in these varieties

Explicit descriptions of irregular threefolds with trivial canonical divisors

Classification based on Albanese morphism properties

Abstract

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.