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arXiv · 2208.12560

Gaussian likelihood geometry of projective varieties

Sandra Di Rocco·Lukas Gustafsson·Luca Schaffler
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Abstract

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.

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Sandra Di Rocco, Lukas Gustafsson, Luca Schaffler. 2022-08-26. Gaussian likelihood geometry of projective varieties. https://arxiv.org/abs/2208.12560

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