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arxiv: 0912.0316 · v2 · submitted 2009-12-02 · 🧮 math.SG · math.AG

Homological mirror symmetry for Brieskorn-Pham singularities

classification 🧮 math.SG math.AG
keywords brieskorn-phamcategorypolynomialsingularitiesabelianassociateddefinedderived
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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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