Linear operators preserving volume polynomials

Volume polynomials are a class of Lorentzian polynomials coming from algebraic geometry. They measure the self intersection number of linear combinations of positive divisors in projective varieties. Compared to Lorentzian polynomials, they have several additional properties. We show that Aluffi's covolume polynomials are precisely the polynomial differential operators preserving volume polynomials. This provides us with a sufficiency criterion for linear operators preserving volume polynomials. We furthermore explore applications to algebraic matroids. This is joint work with June Huh, Mateusz Michałek, Hendrik Süß and Botong Wang.