Linear operators preserving volume polynomials
Algebraic Geometry
2025-06-30 v1 Combinatorics
Abstract
Volume polynomials measure the growth of Minkowski sums of convex bodies and of tensor powers of positive line bundles on projective varieties. We show that Aluffi's covolume polynomials are precisely the polynomial differential operators that preserve volume polynomials, reflecting a duality between homology and cohomology. We then present several applications to matroid theory.
Cite
@article{arxiv.2506.22415,
title = {Linear operators preserving volume polynomials},
author = {Lukas Grund and June Huh and Mateusz Michałek and Hendrik Süss and Botong Wang},
journal= {arXiv preprint arXiv:2506.22415},
year = {2025}
}