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arxiv: 2506.22415 · v1 · pith:PRMXIHR5 · submitted 2025-06-27 · math.AG · math.CO

Linear operators preserving volume polynomials

Lukas Grund , June Huh , Mateusz Micha{\l}ek , Hendrik S\"uss , Botong Wang This is my paper

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classification math.AG math.CO
keywords polynomialsvolumeoperatorsaluffiapplicationsbodiesbundlescohomology
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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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Cited by 2 Pith papers

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    Panel-counting polynomials over topic subsets are Lorentzian, established by an inducing operator that preserves Lorentzian polynomials and realizable volume polynomials.