Dmitri Orlov

Mirror symmetry for weighted projective planes and their noncommutative deformations

The derived categories of coherent sheaves of weighted projective spaces and their noncommutative deformations will be described. We explain how the homological mirror symmetry conjecture looks for the weighted projective planes and show that it holds in this case. Moreover, we also show that this mirror correspondence between derived categories can be extended to toric noncommutative deformations of a weighted projective planes where B-branes are concerned, and their mirror counterparts, non-exact deformations of the symplectic structure of the Landau-Ginzburg where A-branes are concerned.