9 citations · 24 across the 14 of their papers we have counts for
19 papers
Chow polynomials and chain polynomials of matroids are not log-concave
Gergely Bérczi, Basile Coron, Christopher Eur +1
The Hilbert--Poincaré series of the Chow rings of the toric varieties of matroids, often called the \emph{Chow polynomials}, and the -polynomial of their boundary complexes, cal…
Vanishing theorems for combinatorial geometries
Christopher Eur, Alex Fink, Matt Larson
We establish strong vanishing theorems for line bundles on wonderful varieties of hyperplane arrangements, and we show that the resulting positivity properties of Euler characteris…
Canonical forms of oriented matroids
Christopher Eur, Thomas Lam
Positive geometries are semialgebraic sets equipped with a canonical differential form whose residues mirror the boundary structure of the geometry. Every full-dimensional projecti…
K-theoretic positivity for matroids
Christopher Eur, Matt Larson
Hilbert polynomials have positivity properties under favorable conditions. We establish a similar "K-theoretic positivity" for matroids. As an application, for a multiplicity-free…
Multimatroids and rational curves with cyclic action
Emily Clader, Chiara Damiolini, Christopher Eur +2
We study the connection between multimatroids and moduli spaces of rational curves with cyclic action. Multimatroids are generalizations of matroids and delta-matroids introduced b…
Kapranov degrees
Joshua Brakensiek, Christopher Eur, Matt Larson +1
The moduli space of stable rational curves with marked points has two distinguished families of maps: the forgetful maps, given by forgetting some of the markings, and the Kapranov…
Cohomologies of tautological bundles of matroids
Christopher Eur
Tautological bundles of realizations of matroids were introduced in [BEST23] as a unifying geometric model for studying matroids. We compute the cohomologies of exterior and symmet…
K-classes of delta-matroids and equivariant localization
Christopher Eur, Matt Larson, Hunter Spink
Delta-matroids are "type B" generalizations of matroids in the same way that maximal orthogonal Grassmannians are generalizations of Grassmannians. A delta-matroid analogue of the…
Intersection theory of polymatroids
Christopher Eur, Matt Larson
Polymatroids are combinatorial abstractions of subspace arrangements in the same way that matroids are combinatorial abstractions of hyperplane arrangements. By introducing augment…
Essence of independence: Hodge theory of matroids since June Huh
Christopher Eur
Matroids are combinatorial abstractions of independence, a ubiquitous notion that pervades many branches of mathematics. June Huh and his collaborators recently made spectacular br…
Signed permutohedra, delta-matroids, and beyond
Christopher Eur, Alex Fink, Matt Larson +1
We establish a connection between the algebraic geometry of the type B permutohedral toric variety and the combinatorics of delta-matroids. Using this connection, we compute the vo…
Stellahedral geometry of matroids
Christopher Eur, June Huh, Matt Larson
We use the geometry of the stellahedral toric variety to study matroids. We identify the valuative group of matroids with the cohomology ring of the stellahedral toric variety, and…
Tautological classes of matroids
Andrew Berget, Christopher Eur, Hunter Spink +1
We introduce certain torus-equivariant classes on permutohedral varieties which we call "tautological classes of matroids" as a new geometric framework for studying matroids. Using…
The Universal Valuation of Coxeter Matroids
Christopher Eur, Mario Sanchez, Mariel Supina
Coxeter matroids generalize matroids just as flag varieties of Lie groups generalize Grassmannians. Valuations of Coxeter matroids are functions that behave well with respect to su…
Tropical flag varieties
Madeline Brandt, Christopher Eur, Leon Zhang
Flag matroids are combinatorial abstractions of flags of linear subspaces, just as matroids are of linear subspaces. We introduce the flag Dressian as a tropical analogue of the pa…
K-theoretic Tutte polynomials of morphisms of matroids
Rodica Dinu, Christopher Eur, Tim Seynnaeve
We generalize the Tutte polynomial of a matroid to a morphism of matroids via the K-theory of flag varieties. We introduce two different generalizations, and demonstrate that each…
Logarithmic concavity for morphisms of matroids
Christopher Eur, June Huh
Morphisms of matroids are combinatorial abstractions of linear maps and graph homomorphisms. We introduce the notion of basis for morphisms of matroids, and show that its generatin…
Simplicial generation of Chow rings of matroids
Spencer Backman, Christopher Eur, Connor Simpson
We introduce a presentation of the Chow ring of a matroid by a new set of generators, called "simplicial generators." These generators are analogous to nef divisors on projective t…
Divisors on matroids and their volumes
Christopher Eur
The classical volume polynomial in algebraic geometry measures the degrees of ample (and nef) divisors on a smooth projective variety. We introduce an analogous volume polynomial f…