We explore the maximum likelihood degree of a homogeneous polynomial $F$ on a projective variety $X$, $\mathrm{MLD}_F(X)$, which generalizes the concept of Gaussian maximum likelihood degree. We show that $\mathrm{MLD}_F(X)$ is equal to the count of critical points of a rational function on $X$, and give different geometric characterizations of it via topological Euler characteristic, dual varieties, and Chern classes.

翻译：我们探讨射影簇$X$上齐次多项式$F$的最大似然度$\mathrm{MLD}_F(X)$，该概念推广了高斯最大似然度的定义。我们证明$\mathrm{MLD}_F(X)$等于$X$上有理函数临界点的个数，并通过拓扑欧拉示性数、对偶簇及陈类给出其不同的几何刻画。