arXiv subjects

Lukas Grund

Publications and source records attributed to Lukas Grund.

2 recordsLinked to original sources

arXiv2025

Linear operators preserving volume polynomials

We study linear operators preserving the property of being a volume polynomial. More, precisely we show that a linear operator preserves this property if the associated symbol is itself a volume polynomial. This can be seen as an analogue to theorems by Borcea-Brändén and Brändén-Huh for stable polynomials and Lorentzian polynomials, respectively.

math.AG↗

arXiv2025

Linear operators preserving volume polynomials

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.

math.AG↗