×

zbMATH — the first resource for mathematics

Surfaces of class \(\text{VII}_0\) and Hénon automorphisms. (Surfaces de la classe \(\text{VII}_0\) et automorphismes de Hénon.) (French) Zbl 0945.32005
Let \(H:(x,y)\mapsto (x^2+c-ay,x)\) be the Hénon automorphism of \(\mathbb{C}^2\) with coefficients \(a,c\). Compactifying the basin of attraction of \(H\), the authors construct a surface \(S\) with Betti numbers \(b_1=1\), \(b_2=3\). Moreover they show the existence of a non-trivial holomorphic vector field on \(S\) when \(a=2\). This example is quite interesting since the surfaces of the Kodaira class \(\text{VII}_0\) (i.e. with \(b_1=1)\) are not yet classified.
Reviewer: P.Mazet (Paris)

MSC:
32J05 Compactification of analytic spaces
32Q57 Classification theorems for complex manifolds
PDF BibTeX XML Cite
Full Text: DOI