A d-dimensional tensor A of format n×n×⋯×n$n\times n\times \cdots \times n$$n\times n\times \cdots \times n$ defines naturally a rational map Ψ from the projective space Pn−1${\mathbb{P}}^{n-1}$${\mathbb{P}}^{n-1}$ to itself and its eigenscheme is then the subscheme of Pn−1${\mathbb{P}}^{n-1}$ 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.

格式为d维的张量An × n × ⋯ × n$n\times n\times \cdots \times n$$n\times n\times \cdots \times n$从射影空间自然地定义了一个有理图 Ψ磷n − 1${\mathbb{磷}}^{n-1}$${\mathbb{P}}^{n-1}$其自身及其本征方案是磷n − 1${\mathbb{P}}^{n-1}$Ψ 的不动点。特征判别式是A系数中的不可约多项式，对于给定张量，当且仅当其特征方案是奇异的时，该多项式才会消失。在本文中，我们贡献了两个公式来计算n  = 3 和n = 4情况下的特征判别式。 特别是，通过限制对称张量，我们获得了平面曲线和曲面的特征判别式的闭合公式${\mathbb{磷}}^3$作为结果矩阵的一些行列式的比率。