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Funktsional. Anal. i Prilozhen., 2013, Volume 47, Issue 3, Pages 82–87 (Mi faa3120)  

Brief communications

A Resultant System as the Set of Coefficients of a Single Resultant

Ya. V. Abramov

Laboratory of Algebraic Geometry, Higher School of Economics, Moscow

Abstract: Explicit expressions for polynomials forming a homogeneous resultant system of a set of $m+1$ homogeneous polynomial equations in $n+1<m+1$ variables are given. These polynomials are obtained as coefficients of a homogeneous resultant for an appropriate system of $n+1$ equations in $n+1$ variables, which is explicitly constructed from the initial system. Similar results are obtained for mixed resultant systems of sets of $n+1$ sections of line bundles on a projective variety of dimension $n<m$. As an application, an algorithm determining whether one of the orbits under an action of an affine irreducible algebraic group on a quasi-affine variety is contained in the closure of another orbit is described.

Keywords: elimination theory, resultant.

DOI: https://doi.org/10.4213/faa3120

Full text: PDF file (173 kB)
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English version:
Functional Analysis and Its Applications, 2013, 47:3, 233–237

Bibliographic databases:

UDC: 512.718
Received: 30.04.2012

Citation: Ya. V. Abramov, “A Resultant System as the Set of Coefficients of a Single Resultant”, Funktsional. Anal. i Prilozhen., 47:3 (2013), 82–87; Funct. Anal. Appl., 47:3 (2013), 233–237

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