Hermitian symmetric polynomials and CR complexity

Abstract

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.

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

References in corpus (5)

• Normal forms, Hermitian operators, and CR maps of spheres and hyperquadrics
• Complexity results for CR mappings between spheres
• On the complexity of proper holomorphic mappings between balls
• A new gap phenomenon for proper holomorphic mappings from B^n into B^N
• Holomorphic Mappings between Hyperquadrics with Small Signature Difference

Cited by in corpus (5)

• Bounding the rank of Hermitian forms and rigidity for CR mappings of hyperquadrics
• On the existence of holomorphic embeddings of strictly pseudoconvex algebraic hypersurfaces into spheres
• Pfister's theorem fails in the Hermitian case
• Holomorphic maps from the complex unit ball to Type IV classical domains
• On highly degenerate CR maps of spheres