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The Newton complementary dual revisited

André Dória

Departamento de Matemática CCET, Universidade Federal de Sergipe, São Cristovão, Sergipe 49100-000, Brazil

E-mail Address: avsdoria@ufs.br

Corresponding author.

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and

Aron Simis

Departamento de Matemática CCEN, Universidade Federal de Pernambuco, Recife, Pernambuco 50740-640, Brazil

E-mail Address: aron@dmat.ufpe.br

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https://doi.org/10.1142/S0219498818500044Cited by:2 (Source: Crossref)

Abstract

This work deals with the notion of Newton complementary duality as raised originally in the work of the second author and B. Costa. A conceptual revision of the main steps of the notion is accomplished which then leads to a vast simplification and improvement of several statements concerning rational maps and their images. A ring-homomorphism like map is introduced that allows for a close comparison between the respective graphs of a rational map and its Newton dual counterpart.

Communicated by E. Gorla

Keywords:

AMSC: 05E40, 13A99, 14E05, 14E07, 14M25

References

1. B. Costa and A. Simis, New constructions of Cremona maps, Math. Res. Lett. 20 (2013) 629–645. Crossref, Web of Science, Google Scholar
2. W. Decker, G.-M. Greuel, G. Pfister and H. Schönemann, Singular 4-0-2 — A computer algebra system for polynomial computations (2015), http://www.singular.uni-kl.de. Google Scholar
3. I. Pan and A. Simis, Cremona maps of de Jonquières type, Canad. J. Math. 67 (2015) 923–941. Crossref, Web of Science, Google Scholar
4. A. Simis, Cremona transformations and some related algebras, J. Algebra 280(1) (2004) 162–179. Crossref, Web of Science, Google Scholar