Speaker
Araujo Carolina
(IMPA)
Description
In this talk, we discuss the birational geometry of blowups of projective spaces at points in general position. For that, we explore Gale duality -- a correspondence between sets of $n=r+s+2$ points in projective spaces $\mathbb{P}^s$ and $\mathbb{P}^r$. 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. This perspective allows us, in particular, to partially describe the birational geometry of the blowup of $\mathbb{P}^n$ at $n+4$ points in general position. This is a joint work with Ana-Maria Castravet, Inder Kaur and Diletta Martinelli.
Primary author
Araujo Carolina
(IMPA)
