On the geometry of regular maps from a quasi-projective surface to a curve

TL;DR

This paper investigates the geometric properties of regular maps from certain quasi-projective surfaces to curves, focusing on the implications of trivial monodromy and pure mixed Hodge structures.

Contribution

It extends previous results by analyzing the effects of trivial monodromy on the geometry of these surfaces, building on work by Miyanishi, Sugie, Dimca, Zaidenberg, and Kaliman.

Findings

Extended understanding of the geometry of surfaces with trivial monodromy

Connections between monodromy triviality and pure mixed Hodge structures

Generalization of prior results on regular maps from surfaces to curves

Abstract

By exploring the consequences of the triviality of the monodromy group for a class of surfaces of which the mixed Hodge structure is pure, we extend results of Miyanishi and Sugie, Dimca, Zaidenberg and Kaliman.