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The local moduli of Sasaki-Einstein rational homology 7-spheres and invertible polynomials by Valle, Jaime Cuadros; Vicente, Joe Lope is a scholarly article available to read on EtoBox.

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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 Koll\'ar 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-H\"ubsch 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 K\"ahler-Einstein orbifold which in this setting is a rational homology projective 3 -spaces with quotient singularities.

Author

Valle, Jaime Cuadros; Vicente, Joe Lope

Published

2025

Language

EN