Relative Severi inequality for fibrations of maximal Albanese dimension over curves
Forum of Mathematics, Sigma, Tome 10 (2022)
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Let $f: X \to B$ be a relatively minimal fibration of maximal Albanese dimension from a variety X of dimension $n \ge 2$ to a curve B defined 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 fibre F of f has 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.
@article{10_1017_fms_2022_34,
author = {Yong Hu and Tong Zhang},
title = {Relative {Severi} inequality for fibrations of maximal {Albanese} dimension over curves},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {10},
year = {2022},
doi = {10.1017/fms.2022.34},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.34/}
}
TY - JOUR AU - Yong Hu AU - Tong Zhang TI - Relative Severi inequality for fibrations of maximal Albanese dimension over curves JO - Forum of Mathematics, Sigma PY - 2022 VL - 10 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.34/ DO - 10.1017/fms.2022.34 LA - en ID - 10_1017_fms_2022_34 ER -
Yong Hu; Tong Zhang. Relative Severi inequality for fibrations of maximal Albanese dimension over curves. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.34
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