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arXiv · 2404.18341

Slopes of fibrations with trivial vertical fundamental groups

Xiao-Lei Liu·Xin Lu
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Abstract

Kodaira fibrations have non-trivial vertical fundamental groups and their slopes are all $12$. In this paper, we show that $12$ is indeed the sharp upper bound for the slopes of fibrations with trivial vertical fundamental groups. Precisely, for each $g\geq3$ we prove the existence of fibrations of genus $g$ with trivial vertical fundamental groups whose slopes can be arbitrarily close to $12$. This gives a relative analogy of Roulleau-Urz\'ua's work on the slopes of surfaces of general type with trivial fundamental groups.

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Xiao-Lei Liu, Xin Lu. 2024-04-29. Slopes of fibrations with trivial vertical fundamental groups. https://arxiv.org/abs/2404.18341

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