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Localization of automorphisms of some unbounded Levi degenerate algebraic hypersurfaces in ℂn
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G. Dini
Published/Copyright:
July 27, 2005
Abstract
Let D(n, s, k) = {z∈ ℂn : ( –|z1|2 + |z2|2)k + ∑is=3 |zi|2 – ∑in=s+1 |zi|2 < 1}, where k ∈ ℤ+, 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.
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Published Online: 2005-07-27
Published in Print: 2005-04-20
© de Gruyter
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Articles in the same Issue
- Localization of automorphisms of some unbounded Levi degenerate algebraic hypersurfaces in ℂn
- Virtual and non-virtual algebraic Betti numbers
- The classification of flag-transitive Steiner 3-designs
- On surfaces with two apparent double points
- Halphen conditions and postulation of nodes
- Topological affine planes with affine connections
- The embedding of (0, 2)-geometries and semipartial geometries in AG(n, q)
- The geometry of isoparametric hypersurfaces with four distinct principal curvatures in spheres
- New counterexamples to A. D. Alexandrov’s hypothesis
- A maximum principle for parabolic equations on manifolds with cone singularities
- Packing a planar convex body with three homothetical copies and inscribing relatively equilateral triangles
