On the irreducibility of multivariate subresultants
Busé, Laurent ; D'Andrea, Carlos
HAL, inria-00098679 / Harvested from HAL
Text on HAL
Let $P_1,\ldots,P_n$ be generic homogeneous polynomials in $n$ variables of degrees $d_1,\ldots,d_n$ respectively. We prove that if $\nu$ is an integer satisfying ${\sum_{i=1}^n d_i}-n+1-\min\{d_i\}<\nu,$ then all multivariate subresultants associated to the family $P_1,\ldots,P_n$ in degree $\nu$ are irreducible. We show that the lower bound is sharp. As a byproduct, we get a formula for computing the residual resultant of $\binom{\rho-\nu +n-1}{n-1}$ smooth isolated points in $\PP^{n-1}.$
Publié le : 2004-07-05
Classification:  [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC],  [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG],  [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC] 
@article{inria-00098679,
     author = {Bus\'e, Laurent and D'Andrea, Carlos},
     title = {On the irreducibility of multivariate subresultants},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/inria-00098679}
}

Busé, Laurent; D'Andrea, Carlos. On the irreducibility of multivariate subresultants. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/inria-00098679/