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Cousin-I spaces and domains of holomorphy

Ilie Bârză, Viorel Vâjâitu (2009)

Annales Polonici Mathematici

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 X r e g . In particular, Cousin-I proper open sets of ℙ² are Stein. We also study K-envelopes of holomorphy of K-complete spaces.

Coxeter elements for vanishing cycles of types  A 1 2  and  D 1 2

Kyoji Saito (2011)

Annales de l’institut Fourier

We introduce two entire functions f A 1 2 and f D 1 2 in two variables. Both of them have only two critical values 0 and 1 , and the associated maps C 2 C define topologically locally trivial fibrations over C { 0 , 1 } . All critical points in the singular fibers over 0 and 1 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 A 1 2 and D 1 2 , respectively. Coxeter elements of type A 1 2 and...

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