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Moscow Mathematical Journal, 2011, Volume 11, Number 2, Pages 285–315
DOI: https://doi.org/10.17323/1609-4514-2011-11-2-285-315 (Mi mmj422) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Polynomials constant on a hyperplane and CR maps of hyperquadrics

Juří Lebla, Han Petersb

a 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
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DOI: https://doi.org/10.17323/1609-4514-2011-11-2-285-315
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.
Received: October 27, 2009; in revised form August 24, 2010
Bibliographic databases:
Document Type: Article
MSC: 14P99, 05A20, 32H35, 11C08
Language: English
Citation: Juří Lebl, Han Peters, “Polynomials constant on a hyperplane and CR maps of hyperquadrics”, Mosc. Math. J., 11:2 (2011), 285–315
Citation in format AMSBIB
\Bibitem{LebPet11}
\by Ju{\v r}{\'\i}~Lebl, Han~Peters
\paper Polynomials constant on a~hyperplane and CR maps of hyperquadrics
\jour Mosc. Math.~J.
\yr 2011
\vol 11
\issue 2
\pages 285--315
\mathnet{http://mi.mathnet.ru/mmj422}
\crossref{https://doi.org/10.17323/1609-4514-2011-11-2-285-315}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2859238}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000288967100006}
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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