Invariant holomorphic mappings

John P. D'Angelo

Research output: Contribution to journalArticlepeer-review

Abstract

Given a real-analytic hypersurface invariant under a finite unitary group, we construct an invariant holomorphic mapping to a hyperquadric, and prove the basic properties of this mapping. When the hypersurface is the unit sphere, the groups are cyclic, and the quotient is a Lens space, we prove that the coefficients of this mapping must be square roots of integers. For the Lens spaces L(p, p - 1) we evaluate these integers by some combinatorial reasoning. We indicate how these calculations bear on a conjecture about the multiplicity of proper mappings between balls in different dimensions.

Original languageEnglish (US)
JournalJournal of Geometric Analysis
Volume6
Issue number2
StatePublished - 1996

Keywords

  • Finite unitary groups
  • Holomorphic mappings
  • Lens spaces
  • Several complex variables

ASJC Scopus subject areas

  • Geometry and Topology

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