## Talk by Prof. M. Verbitsky: "Holomorphic connections on the space of quasilines"

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Venue: | DM 409 A |

**Speaker:** M. Verbitsky from HSE, Moscow

**Time:** Friday Aug 24, 2012, from 4pm to 5pm in DM409A.

**Title:** "Holomorphic connections on the space of quasilines"

Abstract: A quasiline in a complex manifold M is a holomorphic embedding from CP^1 to M, such that the normal bundle to its image is $O(1)^n$ (such as on the complex line in CP^n). I will construct a holomorphic connection on the space W of quasilines,and prove that its holonomy centralizes a natural holomorphic GL(2)-action on the tangent bundle TW. This kind of geometry is occurs in many geoetric situations, e.g. on the space of mathematical instantons on CP^3. I will explain how this structure is used to prove that the space of mathematical instantons is smooth, solving a classical conjecture of Barth and Hartshorne.

**Time:** Friday, August 24, 2012 @ 04:00 PM

**Venue:** DM 409A