2019/05/21 by Yong Hu, Tong Zhang, Hu, Yong +1
Computer Science · Mathematics · Social Sciences · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #Vietnamese History and Culture Studies
paper · pdf · doi:10.48550/arxiv.1905.08404
openalex publication_date 2019/05/21 · openalex created_date 2022/10/17 · openalex updated_date 2026/07/28
Let f: X → B be a relatively minimal fibration of maximal Albanese dimension from a variety X of dimension n ≥ 2 to a curve B defined over an algebraically closed field of characteristic zero. We prove that KX/Bn ≥ 2n! χf, which was conjectured by Barja in [2]. Via the strategy outlined in [5], it also leads to a new proof of the Severi inequality for varieties of maximal Albanese dimension. Moreover, when the equality holds and χf > 0, we prove that the general fiber F of f has to satisfy the Severi equality that KFn-1 = 2(n-1)! χ(F, ωF). We also prove some sharper results of the same type under extra assumptions.