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Homological mirror symmetry for Brieskorn–Pham singularities

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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.

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

    Masahiro Futaki

  2. Department of Mathematics, Graduate School of Science, Osaka University, Machikaneyama 1-1, Toyonaka, Osaka, 560-0043, Japan

    Kazushi Ueda

Authors
  1. Masahiro Futaki
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  2. Kazushi Ueda
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Correspondence to Masahiro Futaki.

Additional information

This work is supported by Grant-in-Aid for Young Scientists (No.19.8083 and No.20740037) and Engineering and Physical Sciences Research Council (EP/F055366/1).

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Futaki, M., Ueda, K. Homological mirror symmetry for Brieskorn–Pham singularities. Sel. Math. New Ser. 17, 435–452 (2011). https://doi.org/10.1007/s00029-010-0055-6

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