A note on fibrations of Campana general type on surfaces

TL;DR

This paper constructs examples of simply connected surfaces with genus 2 fibrations over the projective line that are of Campana general type, demonstrating new geometric configurations with specific fiber multiplicity properties.

Contribution

It provides explicit constructions of surfaces with genus g fibrations of Campana general type, expanding the known examples in algebraic geometry.

Findings

Constructed simply connected surfaces with genus 2 fibrations of Campana general type.

Fibrations have special fibers with multiplicities ≥ 2 and gcd 1.

Construction extends to any even genus g.

Abstract

We construct examples of simply connected surfaces with genus 2 fibrations over the projective line which are of "general type" according to the definition of Campana. These fibrations have special fibres such that the minimum of the multiplicities of the components is greater or equal to 2 while the g.c.d is 1. We can extend the construction to any even genus g.