Algebraic Geometry notions and the volume polynomial

In this week's seminar, we continue with our previous topic. All the algebraic geometry we have introduced or reviewed so far is ultimately for the purpose of defining the intersection product of divisors (although the definition is quite technical and abstract, the geometric intuition is clear).

We then discussed the polynomial we are interested in studying: the volume polynomial. I wasn't entirely clear on its geometry initially, but our discussion helped clarify this thing much. I plan to look into it a bit further and share more details in the next seminar.

After that, we covered our main theorem:

Theorem 4.6: If \(H_1, \dots, H_n\) are nef divisors on \(Y\), then \(\text{vol}_H(w)\) is a Lorentzian polynomial, and the support of \(\text{vol}_H(w)\) is M-convex.