# Algebraic Geometry Seminar

#### Deformations and BBF form on non-Kähler holomorphically symplectic manifolds

Speaker: Nikon Kurnosov

Location: Warren Weaver Hall 317

Date: Tuesday, April 16, 2019, 3:30 p.m.

Synopsis:

D. Guan has constructed examples of non-Kähler,
simply-connected holomorphically symplectic manifolds from Kodaira surface. Another construction,

using the Hilbert scheme of Kodaira-Thurston surface,

was given by F. Bogomolov. I will discuss deformation theory

of these manifolds, in particular, that holomorphically symplectic deformations

of these manifolds are unobstructed. Using this we obtain local Torelli

theorem, which implies existence of symmetric quadratic form q

on H^2 (M) analogous to BBF-form of hyperkähler manifolds. This is

joint work with M. Verbitsky.