Residual resultant over the projective plane and the implicitization problem
Residual resultant over the projective plane and the implicitization problem
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射影平面上的残差和隐式化问题
DOI：
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发表时间：
2001
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通讯作者：
Laurent Busé
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文献类型：
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作者：
Laurent Busé
在这篇文章中，我们首先将最近的完全交的剩余结式的概念[4]推广到射影平面中余维为2的局部完全交的情况，这是三个多项式的系统在簇的“外部”有解的充分必要条件，这里定义为余维为2的局部完全交。我们在每个多项式的系数中给出它的次数，并将其计算为三个多项式的神或两个行列式除以另一个行列式的乘积。在第二部分中，我们使用这种新类型的结果，给出了一种新的方法来计算的情况下，这些基点是一个局部完全相交的余维2的基点的有理曲面的隐式方程。
In this article, we first generalize the recent notion of residual resultant of a complete intersection [4] to the case of a local complete intersection of codimension 2 in the projective plane, which is the necessary and sufficient condition for a system of three polynomials to have a solution “outside” a variety, defined here by a local complete intersection of codimension 2. We give its degree in the coefficients of each polynomial and compute it as the god of three polynomials or as a product of two determinants divided by another one. In a second part we use this new type of resultant to give a new method to compute the implicit equation of a rational surface with base points in the case where these base points are a local complete intersection of codimension 2.