Seminar

Gale correspondence provides a duality between sets of $n$ points in projective spaces $\mathbb{P}^s$ and $\mathbb{P}^r$ when $n=r+s+2$. For small values of $s$, this duality has a remarkable geometric manifestation: the blowup of $\mathbb{P}^r$ at $n$ points can be realized as a moduli space of vector bundles on the blowup of $\mathbb{P}^s$ 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.