Hyperholomorphic sheaves and deformations of K3 surfaces

by Prof. Sukhendu Mehrotra (CMI, Chennai)

Thursday 31 Jan 2013, 16:00 → 17:00 Asia/Kolkata

AG-69 (Colaba Campus)

I shall report on ongoing joint work with Eyal Markman on generalized deformations of K3 surfaces. Any K3 surface $X$ (for example, a smooth quartic surface in projective space) varies in a 20-dimensional family. On the other hand, the Hilbert scheme $M$ which parametrizes subsets (subchemes) of $n$ points on $X$ is known to deform in a 21-dimensional family. This means that the general deformation of M is not the Hilbert scheme of any K3. How to describe this extra parameter worth of deformations? Our work suggests that they arise from certain ``non-commutative'' deformations of $X$.