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Séminaire Algèbre ICJ

# ANNULE : Hochschild cohomology and deformations of Hilbert schemes ANNULE:(

## by Pieter Belmans (Max Plank Bonn)

jeudi 30 novembre 2017 de au (Europe/Paris)
 Description The Hilbert scheme of n points on a smooth projective surface is again a smooth projective variety, of dimension 2n. It turns out that for del Pezzo surfaces their deformation theory is governed by (non)commutative deformations of the surface. To make this relationship precise one can use fully faithful functors between the derived categories of the surface and the Hilbert scheme. I will explain how these functors are supposed to interact with the Hochschild-Kostant-Rosenberg decomposition, and how noncommutative surfaces give new information about deformations of Hilbert schemes of points.