Generalized resultants over unirational algebraic varieties

Laurent Busé 1 Mohamed Elkadi 1 Bernard Mourrain 1
1 SAGA - Algebraic Systems, Geometry and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this paper, we propose a new method, based on Bezoutian matrices, for computing a nontrivial multiple of the resultant over a projective variety X, which is described on an open subset by a parameterization. This construction, which generalizes the classical and toric one, also applies for instance to blowing up varieties and to residual intersection problems. We recall the classical notion of resultant over a variety X. Then we extend it to varieties which are parameterized on a dense open subset and give new conditions for the existence of the resultant over these varieties. We prove that any maximal nonzero minor of the corresponding Bezoutian matrix yields a nontrivial multiple of the resultant. We end with some experiments.
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Laurent Busé, Mohamed Elkadi, Bernard Mourrain. Generalized resultants over unirational algebraic varieties. Journal of Symbolic Computation, Elsevier, 2000, J. Symbolic Comput., 29 (4-5), pp.515--526. ⟨inria-00096842⟩

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