Geometry of the Gaussian graphical model of the cycle

TL;DR

This paper proves a conjecture about the degree of a projective variety linked to the Gaussian graphical model of a cycle, using advanced intersection theory methods.

Contribution

It introduces new intersection theory techniques to determine the degree of the Gaussian graphical model of a cycle, confirming a conjecture by Sturmfels and Uhler.

Findings

Confirmed the conjecture on the degree of the model.

Developed novel methods based on intersection theory.

Enhanced understanding of the geometry of Gaussian graphical models.

Abstract

We prove a conjecture due to Sturmfels and Uhler concerning the degree of the projective variety associated to the Gaussian graphical model of the cycle. We involve new methods based on the intersection theory in the space of complete quadrics.