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A note on bimodal singularities and mirror symmetry

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Abstract

We discuss the relation between transposition mirror symmetry of Berglund and Hübsch for bimodal singularities and polar duality of Batyrev for associated toric K3 hypersurfaces. We also show that homological mirror symmetry for singularities implies the geometric construction of Coxeter–Dynkin diagrams of bimodal singularities by Ebeling and Ploog.

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Authors and Affiliations

  1. Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji-shi, Tokyo, 192-0397, Japan

    Makiko Mase

  2. Advanced Mathematical Institute, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan

    Makiko Mase

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

    Kazushi Ueda

Authors
  1. Makiko Mase
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  2. Kazushi Ueda
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Correspondence to Makiko Mase.

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Mase, M., Ueda, K. A note on bimodal singularities and mirror symmetry. manuscripta math. 146, 153–177 (2015). https://doi.org/10.1007/s00229-014-0693-7

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  • DOI: https://doi.org/10.1007/s00229-014-0693-7

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