Homological mirror symmetry for Brieskorn–Pham singularities

By M. Futaki, Kazushi Ueda. 2009

61 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d26800a6fa1262b3c13b70d11731e71f2028214b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. P. Seidel

In Geometry and Topology

1. P. Seidel
2. D. Auroux
3. M. Abouzaid
4. I. Smith
5. Alexander F. Ritter
6. Frederick J. Bourgeois III
7. Mark McLean
8. A. Oancea

In Mathematical Physics

1. P. Seidel
2. D. Auroux
3. M. Abouzaid
4. I. Smith
5. Alexander F. Ritter
6. Mark McLean
7. A. Oancea
8. Frederick J. Bourgeois III

Citations in the corpus

• Suspending Lefschetz Fibrations, with an Application to Local Mirror Symmetry (2009, methodology): “Independently of the present work, Futaki and Ueda [6] have applied similar methods to p(x) − yk for k ≥ 2.”