Polynomials constant on a hyperplane and CR maps of hyperquadrics

Details Polynomials constant on a hyperplane and CR maps of hyperquadrics Polynomials constant on a hyperplane and CR maps of hyperquadrics

2009-10-14

arxiv.org/abs/0910.2673v2

Moscow Mathematical Journal, 11 (2011), no. 2, 287-317

Mathematics

Algebraic Geometry

30 pages, 8 figures, to appear in Moscow Mathematical Journal

Scientific paper

We prove a sharp degree bound for polynomials constant on a hyperplane with a fixed number of distinct monomials for dimensions 2 and 3. We study the connection with monomial CR maps of hyperquadrics and prove similar bounds in this setup with emphasis on the case of spheres. The results support generalizing a conjecture on the degree bounds to the more general case of hyperquadrics.

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