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Mosc. Math. J., 2017, Volume 17, Number 4, Pages 717–740 (Mi mmj655)  

The resultant of developed systems of Laurent polynomials

A. G. Khovanskiiab, Leonid Monina

a Department of Mathematics, University of Toronto, Toronto, Canada
b Moscow Independent University, Moscow, Russia

Abstract: Let $R_\Delta(f_1,…,f_{n+1})$ be the $\Delta$-resultant (defined in the paper) of $(n+1)$-tuple of Laurent polynomials. We provide an algorithm for computing $R_\Delta$ assuming that an $n$-tuple $(f_2,…,f_{n+1})$ is developed. We provide a relation between the product of $f_1$ over roots of $f_2=…=f_{n+1}=0$ in $(\mathbf C^*)^n$ and the product of $f_2$ over roots of $f_1=f_3=…=f_{n+1}=0$ in $(\mathbf C^*)^n$ assuming that the $n$-tuple $(f_1f_2,f_3,…,f_{n+1})$ is developed. If all $n$-tuples contained in $(f_1,…,f_{n+1})$ are developed we provide a signed version of Poisson formula for $R_\Delta$. In our proofs we use topological arguments and topological version of the Parshin reciprocity laws.

Key words and phrases: Newton polyhedron, Laurent polynomial, developed system, resultant, Poisson formula, Parshin reciprocity laws.

DOI: https://doi.org/10.17323/1609-4514-2017-17-4-717-740

Full text: http://www.mathjournals.org/.../2017-017-004-008.html
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MSC: 14M25
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Citation: A. G. Khovanskii, Leonid Monin, “The resultant of developed systems of Laurent polynomials”, Mosc. Math. J., 17:4 (2017), 717–740

Citation in format AMSBIB
\Bibitem{KhoMon17}
\by A.~G.~Khovanskii, Leonid~Monin
\paper The resultant of developed systems of Laurent polynomials
\jour Mosc. Math.~J.
\yr 2017
\vol 17
\issue 4
\pages 717--740
\mathnet{http://mi.mathnet.ru/mmj655}
\crossref{https://doi.org/10.17323/1609-4514-2017-17-4-717-740}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000416897600008}


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