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Séminaire DynamiX

École polytechnique – Centre de Mathématiques Laurent Schwartz


10h30-12h00 – Jorge Vitorio Pereira (IMPA)

"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 were 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.