Homological mirror symmetry for punctured spheres

Details Homological mirror symmetry for punctured spheres Homological mirror symmetry for punctured spheres

2011-03-22

arxiv.org/abs/1103.4322v1

Mathematics

Algebraic Geometry

38 pages, 5 figures

Scientific paper

We prove that the wrapped Fukaya category of a punctured sphere ($S^2$ with an arbitrary number of points removed) is equivalent to the triangulated category of singularities of a mirror Landau-Ginzburg model, proving one side of the homological mirror symmetry conjecture in this case. By investigating fractional gradings on these categories, we conclude that cyclic covers on the symplectic side are mirror to orbifold quotients of the Landau-Ginzburg model.

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