Chen Jiang: Algebraic reverse Khovanskii-Teissier inequality via Okounkov bodies

I will discuss the algebraic reverse Khovanskii-Teissier inequality. Namely, let A, B, C be nef divisors on a projective variety of dimension n, then for any integer 1 ≤ k ≤ n-1,

(B^k ∙ A^n–k) ∙ (A^k ∙ C^n–k) ≥ k!(n–k)! / n! (Aⁿ) ∙ (B^k ∙ C^n–k)

The same inequality in the analytic setting was obtained by Lehmann and Xiao for compact Kähler manifolds using the Calabi-Yau theorem, while our approach is purely algebraic using (multipoint) Okounkov bodies.

This is joint work with Zhiyuan Li.

This video was produced by the Japan-US Mathematics Institute and forms part of JAMI Conference 2022.