On the number of fibrations transversal to a rational curve in a complex surface

TL;DR

This paper explores the conditions under which a complex surface admits holomorphic fibrations by discs that are transversal to a rational curve, focusing on their existence and uniqueness.

Contribution

It provides new insights into the existence and non-uniqueness of such fibrations in complex surfaces with rational curves.

Findings

Identifies conditions for the existence of transversal fibrations.

Shows cases where such fibrations are not unique.

Advances understanding of complex surface fibrations.

Abstract

We investigate the existence, and lack of unicity, of a holomorphic fibration by discs transversal to a rational curve in a complex surface.