On higher-rank Khovanskii-Teissier inequalities

TL;DR

This paper generalizes the Khovanskii-Teissier inequality to higher ranks, introduces new Hodge-Riemann relations in mixed settings, and derives related inequalities and log-concavity results.

Contribution

It develops a higher-rank version of the Khovanskii-Teissier inequality and extends Hodge-Riemann relations to new mixed contexts.

Findings

New higher-rank Khovanskii-Teissier inequalities

Extended Hodge-Riemann bilinear relations in mixed settings

Implications for log-concavity and related inequalities

Abstract

We shall discuss a higher-rank Khovanskii-Teissier inequality, generalizing a theorem of Li. In the course of the proof, we develop new Hodge-Riemann bilinear relations in certain mixed settings, which in themselves slightly extend the existing results and imply new Khovanskii-Teissier type inequalities and log-concavity results.