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G. Dini, A. Selvaggi Primicerio

Localization of automorphisms of some unbounded Levi degenerate algebraic hypersurfaces in ?ⁿ

Keywords: Automorphisms, analytic continuation, proper mappings

Let D(n, s, k) = {z? ?ⁿ : ( –|z₁|² + |z₂|²)^k + ?_i^s₌₃ |z_i|² – ?_iⁿ_=s+1 |z_i|² < 1}, where k ? ?⁺, 3 ? s ? n, and let M(n, s, k) = ?D(n, s, k). We determine for any values of n, s and k the biholomorphic automorphisms of D(n, s, k), identifying, in suitable cases, the germs of biholomorphisms that map M(n, s, k) and D(n, s, k) respectively in themselves. It turns out that, if k is even and s = n, any such germ extends to a biholomorphic automorphism of D(n, s, k), while, in other cases, it is a branch of an algebraic correspondence.

Advances in Geometry, Walter de Gruyter

Print ISSN: 1615-715X
Volume: 5, 04/2005
Pages: 171 - 185

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