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arXiv · 2506.22415

Linear operators preserving volume polynomials

Lukas Grund·June Huh·Mateusz Michałek·Hendrik Süss·Botong Wang
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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.

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Lukas Grund, June Huh, Mateusz Michałek, Hendrik Süss, Botong Wang. 2025-06-27. Linear operators preserving volume polynomials. https://arxiv.org/abs/2506.22415

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