Geodesic
A Resultant System as the Set of Coefficients of a Single Resultant
Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 3, pp. 82-87 Cet article a éte moissonné depuis la source Math-Net.Ru

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Explicit expressions for polynomials forming a homogeneous resultant system of a set of $m+1$ homogeneous polynomial equations in $n+1$ 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 $n$. 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. 
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Ya. V. Abramov. A Resultant System as the Set of Coefficients of a Single Resultant. Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 3, pp. 82-87. http://geodesic.mathdoc.fr/item/FAA_2013_47_3_a6/

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