Homological mirror symmetry for Brieskorn-Pham singularities

Abstract

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.

14 pages, 5 figures, v2: improved exposition

References in corpus (5)

• Compact generators in categories of matrix factorizations
• Suspending Lefschetz fibrations, with an application to Local Mirror Symmetry
• Matrix Factorizations and Representations of Quivers I
• Weighted Projective Lines Associated to Regular Systems of Weights of Dual Type
• Homological mirror symmetry of Fermat polynomials

Cited by in corpus (4)

• Suspending Lefschetz fibrations, with an application to Local Mirror Symmetry
• Holography, Matrix Factorizations and K-stability
• Mirror stability conditions and SYZ conjecture for Fermat polynomials
• A note on homological mirror symmetry for singularities of type D