Polynomials constant on a hyperplane and CR maps of spheres

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

2011-05-12

arxiv.org/abs/1105.2343v2

Mathematics

Algebraic Geometry

17 pages, 10 figures; accepted to Illinois J. Math., added 3 figures and improved exposition

Scientific paper

We prove a sharp degree bound for polynomials constant on a hyperplane with a fixed number of nonnegative distinct monomials. This bound was conjectured by John P. D'Angelo, proved in two dimensions by D'Angelo, Kos and Riehl and in three dimensions by the authors. The current work builds upon these results to settle the conjecture in all dimensions. We also give a complete description of all polynomials in dimensions 4 and higher for which the sharp bound is obtained. The results prove the sharp degree bounds for monomial CR mappings of spheres in all dimensions.

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