5 papers · 1 filter
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…
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…
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…
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…
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…