Hermitian symmetric polynomials and CR complexity

Details Hermitian symmetric polynomials and CR complexity Hermitian symmetric polynomials and CR complexity

2010-02-27

arxiv.org/abs/1003.0126v2

Journal of Geometric Analysis, 21 (2011), no. 3, 599-619

Mathematics

Complex Variables

19 pages, latex, fixed typos, to appear in Journal of Geometric Analysis

Scientific paper

10.1007/s12220-010-9160-1

Properties of Hermitian forms are used to investigate several natural questions from CR Geometry. To each Hermitian symmetric polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the polynomial product. We show, except for three trivial cases, that every signature pair can be obtained from the product of two indefinite forms. We provide several new applications to the complexity theory of rational mappings between hyperquadrics, including a stability result about the existence of non-trivial rational mappings from a sphere to a hyperquadric with a given signature pair.

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