This article is cited in 9 papers

Polynomials constant on a hyperplane and CR maps of hyperquadrics

Juří Lebl^a, Han Peters<sup>b

a</sup> Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, USA
^b Korteweg De Vries Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands

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.

Key words and phrases: polynomials constant on a hyperplane, CR mappings of spheres and hyperquadrics, monomial mappings, degree estimates, Newton diagram.

MSC: 14P99, 05A20, 32H35, 11C08

Received: October 27, 2009; in revised form August 24, 2010

Language: English

DOI: 10.17323/1609-4514-2011-11-2-285-315

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