Random algebraic geometry - lecture 2
- Degree and volume. In the second lecture I will try to explain to what extent the right notion of degree, in the probabilistic context, is the notion of volume. I will introduce the classical kinematic formula, over $\mathbb{R}$ and over $\mathbb{C}$, and explain the role of the Veronese variety in this context. In the complex case I will connect to the Bernstein-Khovanskii-Kouchnirenko Theorem.