Polynomials constant on a hyperplane and CR maps of hyperquadrics
Algebraic Geometry
2011-04-14 v2 Combinatorics
Complex Variables
Abstract
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.
Cite
@article{arxiv.0910.2673,
title = {Polynomials constant on a hyperplane and CR maps of hyperquadrics},
author = {Jiri Lebl and Han Peters},
journal= {arXiv preprint arXiv:0910.2673},
year = {2011}
}
Comments
30 pages, 8 figures, to appear in Moscow Mathematical Journal