The self-projecting Grassmannian

Self-dual point configurations have been studied throughout the centuries. In this talk, I will introduce a generalization of these configurations: self-projecting point configurations. These points are parametrized by a subvariety of the Grassmannian, called self-projecting Grassmannian. I will describe how small self-projecting Grassmannians relate to classical moduli spaces, such as moduli spaces of pointed genus g curves.

In the second part of the talk, self-projectivity will be studied from the combinatorial point of view of matroids. In particular, we will introduce self-projective matroids and study their realizability inside the self-projective Grassmannian. I will end with experimental results for the computation of such realization spaces.

Based on joint work with Alheydis Geiger.