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Blow-ups and infinitesimal automorphisms of CR-manifolds

Permanent link
https://hdl.handle.net/10037/20236
DOI
https://doi.org/10.1007/s00209-020-02488-7
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Date
2020-03-07
Type
Journal article
Tidsskriftartikkel
Peer reviewed

Author
Kruglikov, Boris
Abstract
For a real-analytic connected CR-hypersurface M of CR-dimension n⩾1 having a point of Levi-nondegeneracy the following alternative is demonstrated for its symmetry algebra s=s(M): (i) either dims=n2+4n+3 and M is spherical everywhere; (ii) or dims⩽n2+2n+2+δ2,n and in the case of equality M is spherical and has fixed signature of the Levi form in the complement to its Levi-degeneracy locus. A version of this result is proved for the Lie group of global automorphisms of M. Explicit examples of CR-hypersurfaces and their infinitesimal and global automorphisms realizing the bound in (ii) are constructed. We provide many other models with large symmetry using the technique of blow-up, in particular we realize all maximal parabolic subalgebras of the pseudo-unitary algebras as a symmetry.
Publisher
Springer
Citation
Kruglikov BS. Blow-ups and infinitesimal automorphisms of CR-manifolds. Mathematische Zeitschrift. 2020
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