Strict Arakelov inequality for a family of varieties of general type

Xin Lu; Jinbang Yang; Kang Zuo

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arXiv · 2104.08756

Strict Arakelov inequality for a family of varieties of general type

Xin Lu·Jinbang Yang·Kang Zuo

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Abstract

Let $f:\, X\to Y$ be a semistable non-isotrivial family of $n$-folds over a smooth projective curve with discriminant locus $S \subseteq Y$ and with general fibre $F$ of general type. We show the strict Arakelov inequality \[\frac{\mathrm{deg}\, f_*\omega_{X/Y}^\nu}{\mathrm{rank}\, f_*\omega_{X/Y}^\nu} < {n\nu\over 2}\cdot\mathrm{deg}\,\Omega^1_Y(\log S),\] for all $\nu\in \mathbb N$ such that the $\nu$-th pluricanonical linear system $|\omega^\nu_F|$ is birational. This answers a question asked by M\"oller, Viehweg and the third named author.

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BibTeX RIS

Xin Lu, Jinbang Yang, Kang Zuo. 2021-04-18. Strict Arakelov inequality for a family of varieties of general type. https://arxiv.org/abs/2104.08756

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