Calabi Yau Hypersurfaces and SU-Bordism

  • Ivan Yu. LimonchenkoEmail author
  • Zhi Lü
  • Taras E. Panov


V. V. Batyrev constructed a family of Calabi–Yau hypersurfaces dual to the first Chern class in toric Fano varieties. Using this construction, we introduce a family of Calabi–Yau manifolds whose SU-bordism classes generate the special unitary bordism ring \({\Omega ^{SU}}[\frac{1}{2}] \cong Z[\frac{1}{2}][{y_i}:i \geqslant 2]\). We also describe explicit Calabi–Yau representatives for multiplicative generators of the SU-bordism ring in low dimensions.


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • Ivan Yu. Limonchenko
    • 1
    Email author
  • Zhi Lü
    • 1
  • Taras E. Panov
    • 2
    • 3
    • 4
  1. 1.School of Mathematical SciencesFudan UniversityShanghaiP.R. China
  2. 2.Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  3. 3.Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of National Research Centre “Kurchatov Institute,”MoscowRussia
  4. 4.Institute for Information Transmission Problems (Kharkevich Institute)Russian Academy of Sciences, Bol’shoi Karetnyi per. 19MoscowRussia

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