Diletta Martinelli

Title: Gale duality, blowups and moduli spaces

Abstract:
The Gale correspondence provides a duality between sets of n points in
projective spaces P^s and P^r when n=r+s+2. For small values of s, this
duality has a remarkable geometric manifestation: the blowup of P^r at n
points can be realized as a moduli space of vector bundles on the blowup
of P^s at the Gale dual points. We explore this realization to describe
the birational geometry of blowups of projective spaces at points in
very general position. We will focus in particular on the cases where
the blowup fails to be a Mori Dream Space, reporting on a joint work
with Carolina Araujo, Ana-Maria Castravet and Inder Kaur.