Homological mirror symmetry for punctured spheres
Algebraic Geometry
2014-05-14 v2 Symplectic Geometry
Abstract
We prove that the wrapped Fukaya category of a punctured sphere ( 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.
Keywords
Cite
@article{arxiv.1103.4322,
title = {Homological mirror symmetry for punctured spheres},
author = {Mohammed Abouzaid and Denis Auroux and Alexander I. Efimov and Ludmil Katzarkov and Dmitri Orlov},
journal= {arXiv preprint arXiv:1103.4322},
year = {2014}
}
Comments
38 pages, 5 figures; v2: minor revisions (similar to published version)