Homological mirror symmetry for Brieskorn-Pham singularities

Details Homological mirror symmetry for Brieskorn-Pham singularities Homological mirror symmetry for Brieskorn-Pham singularities

2009-12-02

arxiv.org/abs/0912.0316v2

Mathematics

Symplectic Geometry

14 pages, 5 figures, v2: improved exposition

Scientific paper

We prove that the derived Fukaya category of the Lefschetz fibration defined
by a Brieskorn-Pham polynomial is equivalent to the triangulated category of
singularities associated with the same polynomial together with a grading by an
abelian group of rank one. Symplectic Picard-Lefschetz theory developed by
Seidel is an essential ingredient of the proof.

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