Space of self-dual configurations

The Gale transform is an intriguing map between spaces of point configurations in projective spaces. A point configuration is called self-dual if its Gale transform is equivalent to the configuration itself. In this talk, I report recent work in progress with Alessio Caminata and Luca Schaffler on algebraic/geometric properties of the space of self-dual configurations. We provide set-theoretic defining equations and show that its normalization is almost Gorenstein.