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Moscow Mathematical Journal

Volume 17, Issue 4, October–December 2017  pp. 717–740.

The Resultant of Developed Systems of Laurent Polynomials

Authors:  A. G. Khovanskii (1) and Leonid Monin (2)
Author institution:(1) Department of Mathematics, University of Toronto, Toronto, Canada; Moscow Independent University, Moscow, Russia
(2) Department of Mathematics, University of Toronto, Toronto, Canada


Let RΔ(f1, ..., fn+1) be the Δ-resultant (defined in the paper) of (n+1)-tuple of Laurent polynomials. We provide an algorithm for computing RΔ assuming that an n-tuple (f2, ..., fn+1) is developed. We provide a relation between the product of f1 over roots of f2 = ··· = fn+1 = 0 in (C*)n and the product of f2 over roots of f1 = f3 = ··· = fn+1 = 0 in (C*)n assuming that the n-tuple (f1f2, f3, ..., fn+1) is developed. If all n-tuples contained in (f1, ..., fn+1) are developed we provide a signed version of Poisson formula for RΔ. In our proofs we use topological arguments and topological version of the Parshin reciprocity laws.

2010 Math. Subj. Class. 14M25.

Keywords: Newton polyhedron, Laurent polynomial, developed system, resultant, Poisson formula, Parshin reciprocity laws.

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