迭代和混合判别式
Iterated and mixed discriminants
摘要：
我们考虑了支持在不动点配置上的Laurent多项式系统。在非亏损的情况下，封闭的轨迹的系数给出一个非退化的重根的系统是由一个多项式定义的混合判别式。我们定义了一个相关的多项式称为多元迭代判别式，推广了经典的Schäfli超行列式方法。这种迭代判别式更容易计算，我们证明了它总是整除的混合判别式。我们表明，切线交点可以通过迭代计算，当且仅当相应的对偶品种的奇异轨迹有足够高的余维。我们还研究了Segre-Veronese簇和平面光滑多边形的格点对应的点配置的迭代判别式与混合判别式的等价性。
英文摘要：
We consider systems of Laurent polynomials with support on a fixed point configuration. In the non-defective case, the closure of the locus of coefficients giving a non-degenerate multiple root of the system is defined by a polynomial called the mixed discriminant. We define a related polynomial called the multivariate iterated discriminant, generalizing the classical Schäfli method for hyperdeterminants. This iterated discriminant is easier to compute and we prove that it is always divisible by the mixed discriminant. We show that tangent intersections can be computed via iteration if and only if the singular locus of a corresponding dual variety has sufficiently high codimension. We also study when point configurations corresponding to Segre-Veronese varieties and to the lattice points of planar smooth polygons, have their iterated discriminant equal to their mixed discriminant.
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