@article{Lu2022, 
author = {Xin Lu and Jinbang Yang and Kang Zuo},
title = {Strict Arakelov inequality for a family of varieties of general type},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {7},
pages = {2643-2662},
keywords = {Arakelov inequality, family},
url = {https://www.sciopen.com/article/10.3934/era.2022135},
doi = {10.3934/era.2022135},
abstract = {Let  f:X→Y be a semistable non-isotrivial family of  n-folds over a smooth projective curve with discriminant locus  S⊆Y and with general fiber  F of general type. We show the strict Arakelov inequality   deg⁡f∗ωX/Yνrankf∗ωX/Yν<nν2⋅deg⁡ΩY1(log⁡S),for all  ν∈N such that the  ν-th pluricanonical linear system  |ωFν| is birational. This answers a question asked by Möller, Viehweg and the third named author [1].}
}