Invariant holomorphic mappings |
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Authors: | John P D’Angela |
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Institution: | 1. Department of Mathematics, University of Illinois, 61801, Urbana, IL
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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 spacesL(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. |
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