It was proven that if the modal path corresponding to ρM(p)>0 coincides with a part of the algebraic variety V, then the geometric properties of V can be determined by the analytical behavior of the modal density distribution, such as curvature and singularity distribution.
Yu Wei responded quickly, clearly remembering the content of that class very well.
"Oh, then it should be analyzing the embedding behavior of algebraic varieties in Modal Space. What else was there?" Qiao Yu continued to ask.
"There was, like the isomorphism between modal paths and torus mapping, and the intersection properties of modal paths and algebraic curves. But he only mentioned these during class and didn't go in-depth, and these topics weren't included in the exams. He said if we want to study this, it should be at the graduate level."
Qiao Yu nodded, and in just a few conversations, he had already finished the review and abstract of the paper and started reading the main text.
