论文标题
三元和第四纪特征歧义的公式
Formulas for the eigendiscriminants of ternary and quaternary forms
论文作者
论文摘要
a $ d $ - 维张$ a $ a $ a $ n \ times n \ times n \ times \ cdots \ times n $自然定义了从投射空间$ \ mathbb {p}^{n-1} $的理性映射$ψ$，然后向$ \ mathbb {p} $ n o;特征歧义是在$ a $的系数中的一种不可约多的多项式，当它的特征性是单数时，对于给定的张量而言，它消失了。在本文中，我们为计算特征性歧义因子的计算$ n = 3 $和$ n = 4 $贡献了两个公式。特别是，通过限制对称张量，我们获得了$ \ mathbb {p}^3 $中平面曲线和表面的特征歧义的封闭公式，作为所得矩阵的某些决定因素的比率。
A $d$-dimensional tensor $A$ of format $n\times n\times \cdots \times n$ defines naturally a rational map $Ψ$ from the projective space $\mathbb{P}^{n-1}$ to itself and its eigenscheme is then the subscheme of $\mathbb{P}^{n-1}$ of fixed points of $Ψ$. The eigendiscriminant is an irreducible polynomial in the coefficients of $A$ that vanishes for a given tensor if and only if its eigenscheme is singular. In this paper we contribute two formulas for the computation of eigendiscriminants in the cases $n=3$ and $n=4$. In particular, by restriction to symmetric tensors, we obtain closed formulas for the eigendiscriminants of plane curves and surfaces in $\mathbb{P}^3$ as the ratio of some determinants of resultant matrices.
