Slopes of fibrations with trivial vertical fundamental groups

Autor:	Liu, Xiao-Lei, Lu, Xin
Rok vydání:	2024
Předmět:	Mathematics - Algebraic Geometry
Druh dokumentu:	Working Paper
Popis:	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. Comment: Any comment is warmly welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.18341 Zobrazit plný text záznamu View this record from Arxiv