Slopes of fibrations with trivial vertical fundamental groups

Xiao-Lei Liu; Xin Lu

Slopes of fibrations with trivial vertical fundamental groups

Algebraic Geometry 2024-04-30 v1

Authors: Xiao-Lei Liu , Xin Lu

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.

Keywords

Kodaira fibrations vertical fundamental groups slopes of fibrations genus g fibrations sharp upper bound surfaces of general type

Cite

@article{arxiv.2404.18341,
  title  = {Slopes of fibrations with trivial vertical fundamental groups},
  author = {Xiao-Lei Liu and Xin Lu},
  journal= {arXiv preprint arXiv:2404.18341},
  year   = {2024}
}

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Slopes of fibrations with trivial vertical fundamental groups

Abstract

Keywords

Cite

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