Realizing self-projecting Matroids

Self-dual point configurations have been studied throughout the centuries. In this talk the generalization to self-projecting point configurations will be introduced. These give rise to self-projecting matroids, in other words, to matroids that satisfy the disjoint bases property and that have no almost generic element. The parameter space of self-projecting point configurations is the self-projecting Grassmannian. This is also the space of self-projecting realizations of self-projecting matroids. Its structure is interesting from multiple perspectives, like mathematica physics. We compute the realization spaces for small matroids up to rank 4 on 9 elements. If time permits, a short overview of the available code and database will be given. I will finish with an outlook on the perspective of tropical geometry and subdivisions of matroid polytopes.

This project is joint work in progress with Francesca Zaffalon.