Resultant over the residual of a complete intersection

In this article, we study the residual resultant which is the necessary and sufficient condition for a polynomial system F to have a solution in the residual of a variety, defined here by a complete intersection G. We show that it corresponds to an irreducible divisor and give an explicit formula fo...

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Vydáno v:Journal of pure and applied algebra Ročník 164; číslo 1; s. 35 - 57
Hlavní autoři: Busé, L., Elkadi, M., Mourrain, B.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 24.10.2001
Elsevier
Edice:Effective methods in algebraic geometry (Bath, 2000)
Témata:
Algebraic Geometry
Commutative Algebra
Computer Science
Mathematics
Symbolic Computation
13F20
68W30
11C
13P
14Q
ISSN:0022-4049, 1873-1376
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Popis
Shrnutí:In this article, we study the residual resultant which is the necessary and sufficient condition for a polynomial system F to have a solution in the residual of a variety, defined here by a complete intersection G. We show that it corresponds to an irreducible divisor and give an explicit formula for its degree in the coefficients of each polynomial. Using the resolution of the ideal (F : G) and computing its regularity, we give a method for computing the residual resultant using a matrix which involves a Macaulay and a Bezout part. In particular, we show that this resultant is the gcd of all the maximal minors of this matrix. We illustrate our approach for the residual of points and end by some explicit examples.
ISSN:0022-4049
1873-1376
DOI:10.1016/S0022-4049(00)00144-4