Семинар лаборатории алгебраической геометрии: Артур Томберг

На семинаре выступит Artour Tomberg (University of Western Ontario) с докладом Fibrewise stable bundles on twistor spaces of hyperkahler manifolds

A hyperkahler structure on a smooth manifold M consists a triple of integrable almost complex structures (I, J, K) that satisfy quaternionic relations I^2 = J^2 = K^2 = -1, IJ = -JI = K, and a metric g which is Kahler with respect to I, J and K simultaneously. By taking linear combinations of I, J and K with coefficients whose squares sum up to one, we get a sphere S^2 of induced complex structures on M, and we define the twistor space Tw(M) to be the cartesian product of M and S^2. Identifying S^2 with CP^1 in the usual way, there is a natural complex structure on the manifold Tw(M), with respect to which the projection Tw(M) -> CP^1 is holomorphic. I will talk about the relationship between stability of a holomorphic vector bundle E on Tw(M) and its fibrewise stability, that is, stability of its restrictions to the fibres of the holomorphic twistor projection Tw(M) -> CP^1.