Courbes entières dans les surfaces algébriques complexes
We prove that a Cousin-I open set D of an irreducible projective surface X is locally Stein at every boundary point which lies in . In particular, Cousin-I proper open sets of ℙ² are Stein. We also study K-envelopes of holomorphy of K-complete spaces.
We introduce two entire functions and in two variables. Both of them have only two critical values and , and the associated maps define topologically locally trivial fibrations over . All critical points in the singular fibers over and are ordinary double points, and the associated vanishing cycles span the middle homology group of the general fiber, whose intersection diagram forms bi-partitely decomposed infinite quivers of type and , respectively. Coxeter elements of type and...