5 papers
Counting point configurations in projective space
Alex Fink, Navid Nabijou, Rob Silversmith
We investigate the enumerative geometry of point configurations in projective space. We define "projective configuration counts": these enumerate configurations of points in projec…
Quadratic exchange equations for Coxeter matroids
Kieran Calvert, Aram Dermenjian, Alex Fink +1
Tropicalisation (with trivial coefficients) is a process that turns a polynomial equation into a combinatorial predicate on subsets of the set of variables. We show that for each m…
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…
The polytope of all matroids
Luis Ferroni, Alex Fink
It is possible to write the indicator function of any matroid polytope as an integer combination of indicator functions of Schubert matroid polytopes. In this way, every matroid on…
The external activity complex of a pair of matroids
Andrew Berget, Alex Fink
We introduce the Schubert variety of a pair of linear subspaces in and the external activity complex of a pair of not necessarily realizable matroids. Both of these…