2025/03/24 by Valle, Jaime Cuadros, Vicente, Joe Lope
#32G07 #32G13 #53C25 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.18650
We compute the dimension of the local moduli space of Sasaki-Einstein metrics for links of invertible polynomials coming from the list of Johnson and Kollár of anticanonically embedded Fano 3-folds of index 1 that produce rational homology 7-spheres, that is, 7-manifolds whose rational-homology equals that of the 7-sphere. In order to do so, we propose additional conditions to the Diophantine equations associated to this problem. We also find solutions for the problem associated to the moduli for the Berglund-Hübsch duals of links arising from Thom-Sebastiani sums of chain and cycle polynomials. In particular we give an explicit description of local moduli of the complex structure for the corresponding Kähler-Einstein orbifold which in this setting is a rational homology projective 3 -spaces with quotient singularities.