An introduction to the deformation of Hilb P2

Chunyi Li

The deformation of the Hilbert scheme of points on the projective plane is first constructed in the paper of Nevins and Stafford by an approach of non-commutative geometry. In 2011, Hitchin reintroduces the construction by an approach from Poisson geometry. In addition, he shows that the construction by Nevins and Stafford is `versal', i.e., all the deformations of the Hilbert scheme are constructed in their way. I will briefly introduce these constructions through an example of Hilb^2 P_2, and talk about my work/joint work on the deformation of Hilbert scheme of del Pezzo surface, as well as an interesting result on the minimal model program of the deformation of Hilb^n P_2

http://scgp.stonybrook.edu/video_portal/video.php?id=903

Simons- Workshop: Graduate Workshop on Geometry of Hilbert schemes