On morphisms into contractible surfaces of Kodaira logarithmic dimension 1 (Q1363228)

The authors describe all morphisms from \({\mathbb{C}}\) into contractible surfaces of Kodaira dimension 1. In particular, a complete classification of morphisms from a once-punctured Riemann surface into a contractible surface as before is obtained. As a consequence, if \(f\) is a regular function on a contractible surface of Kodaira dimension 1, whose zero fiber is isomorphic to a once-punctured Riemann surface, then every fiber of \(f\) has exactly one puncture.