Polynomials constant on a hyperplane and CR maps of spheres
Algebraic Geometry
2013-12-05 v2 Combinatorics
Complex Variables
Abstract
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.
Cite
@article{arxiv.1105.2343,
title = {Polynomials constant on a hyperplane and CR maps of spheres},
author = {Jiri Lebl and Han Peters},
journal= {arXiv preprint arXiv:1105.2343},
year = {2013}
}
Comments
17 pages, 10 figures; accepted to Illinois J. Math., added 3 figures and improved exposition