Speaker: Jorge Vitório Pereira (IMPA, Brazil) Date: 12/11/2021 at 10:30 Title: On the formal principle for curves on projective spaces Abstract: Classical results by Grauert and collaborators guarantee that analytic equivalence classes of germs of smooth surfaces along a compact smooth curve of positive or negative self-intersection are determined by their formal equivalence classes. Germs of smooth surfaces along a compact smooth curve of zero self-intersection behave differently. There are formal equivalence classes with infinite-dimensional analytic moduli according to recent results by Loray, Thom, and Touzet. I will discuss a joint work with Olivier Thom where we prove that the formal completion of a complex projective surface along a rigid smooth curve with trivial normal bundle determines the birational equivalence class of the projective surface."