Abstract
AbstractLet$f: X \to B$be a relatively minimal fibration of maximal Albanese dimension from a varietyXof dimension$n \ge 2$to a curveBdefined over an algebraically closed field of characteristic zero. We prove that$K_{X/B}^n \ge 2n! \chi _f$. It verifies a conjectural formulation of Barja in [2]. Via the strategy outlined in [4], it also leads to a new proof of the Severi inequality for varieties of maximal Albanese dimension. Moreover, when the equality holds and$\chi _f> 0$, we prove that the general fibreFoffhas to satisfy the Severi equality that$K_F^{n-1} = 2(n-1)! \chi (F, \omega _F)$. We also prove some sharper results of the same type under extra assumptions.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis