Cartan-Chern-Moser theory on algebraic hypersurfaces and an application to the study of automorphism groups of algebraic domains

Xiaojun Huang, Shanyu Ji

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

For a strongly pseudoconvex domain D ⊂ ℂn+1 defined by real polynoinial of degree k0, we prove that the Lie group Aut(D) can be identified with a constructible Nash algebraic smooth variety in the CR structure bundle Y of ∂D and that the sum of its Betti numbers is bounded by a certain constant Cn,k0 depending only on n and k0. In case D is simply connected, we further give an explicit but quite rough bound in terms of the dimension and the degree of the defining polynomial. Our approach is to adapt the Cartan-Chern-Moser theory to the algebraic hypersurfaces.

Original languageEnglish (US)
Pages (from-to)1793-1831+X-XI+VII
JournalAnnales de l'Institut Fourier
Volume52
Issue number6
DOIs
StatePublished - 2002

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology

Keywords

  • Algebraic domains
  • Automorphism group
  • Betti numbers
  • Cartan-Chern-Moser theory
  • Real algebraic hypersurface
  • Strongly pseudoconvex domain

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