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Session S35 - Moduli Spaces in Algebraic Geometry and Applications

Tuesday, July 20, 16:00 ~ 16:40 UTC-3

Gale Duality, Blowups and Moduli Spaces

Carolina Araujo

IMPA, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

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.

Joint work with Ana-Maria Castravet (University of Versailles, France), Inder Kaur (PUC-Rio, Brazil) and Diletta Martinelli (University of Amsterdam, Netherlands).

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