Gale duality, blow-ups and moduli spaces

par Ana-Maria Castravet (Université de Versailles Saint-Quentin-en-Yvelines)

jeudi 17 sept. 2026, 14:00 → 16:00 Europe/Paris

I will discuss joint work with Carolina Araujo, Inder Kaur and Diletta Martinelli about the birational geometry of blow-ups of projective spaces at points in general position.  We will explore Gale duality, a correspondence between sets of n=r+s+2  points in projective spaces P^r and P^s. For small values of s, this duality has a remarkable geometric manifestation: the blow-up of P^r at n points can be realized as a moduli space of vector bundles on the blow-up of P^s at the Gale dual points. One can then exploit this for understanding the birational geometry of this space.