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.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 47, No. 3, pp. 82–87, 2013
Original Russian Text Copyright © by Ya. V. Abramov
This work was supported in part by the Laboratory of Algebraic Geometry, Higher School of Economics (grant no. RF 11.G34.31.0023) and by RFBR grants nos. 10-01-00836, 12-01-33101, and 12-01-31233.
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Abramov, Y.V. A resultant system as the set of coefficients of a single resultant. Funct Anal Its Appl 47, 233–237 (2013). https://doi.org/10.1007/s10688-013-0029-5
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DOI: https://doi.org/10.1007/s10688-013-0029-5