Berglund–Hübsch Transpose Rule And Sasakian Geometry

Authors

Ralph R. Gomez, Swarthmore CollegeFollow

Document Type

Article

Publication Date

2024

Published In

Annals Of Global Analysis And Geometry

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.

Keywords

Sasakian, Fano, Orbifold, Einstein

Comments

This work is a preprint that is freely available courtesy of Springer. The version of record can be freely accessed via SpringerNature's SharedIt service.

Recommended Citation

Ralph R. Gomez. (2024). "Berglund–Hübsch Transpose Rule And Sasakian Geometry". Annals Of Global Analysis And Geometry. Volume 65, DOI: 10.1007/s10455-023-09932-x
https://works.swarthmore.edu/fac-math-stat/276