2022/10/07 by Gomez, Ralph R.
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2210.03577
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 exists four seven dimensional Sasakian manifolds of positive Ricci curvature, two of which are actually Sasaki-Einstein.