4 papers
The Gröbner Version of White's Conjecture is False
Spencer Backman, Nathan Cheung, Michał Lasoń +2
We show that the toric ideal of the Fano matroid polytope does not have a quadratic Gröbner basis. This resolves in the negative a strong version of White's conjecture from matroid…
Vertex Posets, Monotone Path Polytopes, and Chow Polynomials
Mateusz Michałek, Leonid Monin, Botong Wang
Let be a convex polytope and let be a linear functional which is nonconstant on every edge of . The induced acyclic orientation determines positive…
Linear operators preserving volume polynomials
Lukas Grund, June Huh, Mateusz Michałek +2
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 polyn…
Realizations of homology classes and projection areas
Daoji Huang, June Huh, Mateusz Michałek +2
The relationship between convex geometry and algebraic geometry has deep historical roots, tracing back to classical works in enumerative geometry. In this paper, we continue this…