School of Mathematics Seminars and Lectures
Hyperholomorphic sheaves and deformations of K3 surfaces
by Prof. Sukhendu Mehrotra (CMI, Chennai)
Thursday, January 31, 2013
from
to
(Asia/Kolkata)
at Colaba Campus ( AG-69 )
at Colaba Campus ( AG-69 )
Description |
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 $X$. |