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arXiv · 2402.14516

Upper bounds on the genus of hyperelliptic Albanese fibrations

Songbo Ling·Xin Lü
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Abstract

Let $S$ be a minimal irregular surface of general type, whose Albanese map induces a hyperelliptic fibration $f:\,S \to B$ of genus $g$.We prove a quadratic upper bound on the genus $g$, i.e., $g\leq h\big(\chi(\mathcal{O}_S)\big)$, where $h$ is a quadratic function. We also construct examples showing that the quadratic upper bounds can not be improved to the linear ones. In the special case when $p_g(S)=q(S)=1$, we show that $g\leq 14$.

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Songbo Ling, Xin Lü. 2024-02-22. Upper bounds on the genus of hyperelliptic Albanese fibrations. https://doi.org/10.1017/fms.2025.43

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