Abstract
We apply the Berglund–Hübsch transpose rule from BHK mirror symmetry to show that to an \(n-1\)-dimensional Calabi–Yau orbifold in weighted projective space defined by an invertible polynomial, we can associate four (possibly) distinct Sasaki manifolds of dimension \(2n+1\) which are \(n-1\)-connected and admit a metric of positive Ricci curvature. We apply this theorem to show that for a given K3 orbifold, there exist four seven-dimensional Sasakian manifolds of positive Ricci curvature, two of which are actually Sasaki–Einstein.
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Acknowledgements
I would like to thank Marco Aldi for suggesting to me the idea of looking into how ideas from BHK mirror symmetry might be used in Sasakian geometry. I also would like to thank Christina Tønneson-Friedman for useful conversations and encouragement in writing this article. Parts of this article were written while attending the Union College Mathematics Conference 2022, so I want to thank the organizers for creating such a hospitable place to share ideas. I would also like to thank Jaime Cuadros Valle and Tyler Kelly for useful conversations. I would also like to thank the referee for invaluable suggestions which improved the quality of the paper. Finally, I would like to thank the Lang Faculty fellowship from Swarthmore College.
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Gomez, R.R. Berglund–Hübsch transpose rule and Sasakian geometry. Ann Glob Anal Geom 65, 2 (2024). https://doi.org/10.1007/s10455-023-09932-x
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DOI: https://doi.org/10.1007/s10455-023-09932-x