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J-holomorphic curves in a nef class

Weiyi Zhang
(University of Michigan)
Tuesday, 26 March, 2013, at 16:00-17:00, in Aud. D3 (1531-215)
After explaining complexity of arbitrary reducible subvariety when the ambient manifold is of dimension 4, we offer an upper bound of the total genus of a J-holomorphic subvariety when the class of the subvariety is J-nef. It seems new even when J is integrable. For a spherical class, it has particularly strong consequences. It is shown that, for any tamed J, each irreducible component is a smooth rational curve. We completely classify configurations of maximal dimension. To prove these results, we treat subvarieties as weighted graphs and introduce several combinatorial moves. This is a joint work with Tian-Jun Li.
Organised by: QGM
Contact person: Jørgen Ellegaard Andersen