B\'ezout type inequality in convex geometry

TL;DR

This paper establishes a Bézout type inequality for mixed volumes in convex geometry, extending the theoretical framework and connecting it with complex geometry through a reverse Khovanskii-Teissier inequality.

Contribution

It introduces a new inequality for mixed volumes of convex bodies, inspired by complex geometry, and builds on previous work on reverse inequalities.

Findings

Proves a Bézout type inequality for mixed volumes.

Connects convex geometry with complex geometry via reverse inequalities.

Extends the theoretical understanding of mixed volumes.

Abstract

We give a B\'ezout type inequality for mixed volumes, which holds true for any convex bodies. The key ingredient is the reverse Khovanskii-Teissier inequality for convex bodies, which was obtained in our previous work and inspired by its correspondence in complex geometry.