Three Proofs of the Reverse Khovanskii-Teissier Inequality

Explore a mathematical lecture that presents three distinct proofs of the reverse Khovanskii-Teissier inequality for nef divisors, a significant theorem in Kähler geometry. Delve into the historical development of this three-term inequality, from its initial observations by Xiao and Popovici in the context of Morse type inequalities to its extensions by Lehman and Xiao for mixed volumes of convex bodies, and Jiang and Li's proof for projective varieties using Okounkov bodies. Learn how this inequality provides an upper bound on the product of two divisors through their relationship with a third divisor, distinguishing it from the standard Khovanskii-Teissier inequality. Master the three fundamental approaches to proving this inequality: analytic, algebraic, and convex geometric methods, each offering unique insights into this mathematical relationship.