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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