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Seminar

BGMS Seminar: Gale duality, blowups and moduli spaces May 13, 2019 (11:30 AM PDT - 12:30 PM PDT)
Parent Program: Birational Geometry and Moduli Spaces MSRI: Simons Auditorium
Speaker(s) Carolina Araujo (Institute of Pure and Applied Mathematics (IMPA))
Description No Description
Video
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.