Beglund-Hübsch transpose and Sasaki-Einstein rational homology 7-spheres
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| Format: | Preprint |
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2023
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| _version_ | 1866914948964155392 |
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| author | Valle, Jaime Cuadros Gomez, Ralph R. Vicente, Joe Lope |
| author_facet | Valle, Jaime Cuadros Gomez, Ralph R. Vicente, Joe Lope |
| contents | We show that links of invertible polynomials coming from the Johnson and Kollár list of Kähler-Einstein 3-folds that are rational homology 7-spheres remain rational homology 7-spheres under the so-called Berglund-Hübsch transpose rule coming from classical mirror symmetry constructions. Actually, this rule produces twins, that is, links with same degree, Milnor number and homology H_3, with the exception of iterated Thom-Sebastiani sums of singularities of chain and cycle type, where the torsion and the Milnor number may vary. The Berglund-Hübsch transpose rule not only gives a framework to better understand the existence of SasakiEinstein twins but also gives a mechanism for producing new examples of Sasaki-Einstein twins in the rational homology 7 -sphere setting. We also give reasonable conditions for a Sasaki-Einstein rational homology 7-sphere to remain Sasaki-Einstein under the BH-transpose rule. In particular, we found 75 new examples of Sasaki-Einstein rational homology 7-spheres arising as links of not well-formed hypersurface singularities. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_15998 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Beglund-Hübsch transpose and Sasaki-Einstein rational homology 7-spheres Valle, Jaime Cuadros Gomez, Ralph R. Vicente, Joe Lope Differential Geometry 53C25, 57R60 We show that links of invertible polynomials coming from the Johnson and Kollár list of Kähler-Einstein 3-folds that are rational homology 7-spheres remain rational homology 7-spheres under the so-called Berglund-Hübsch transpose rule coming from classical mirror symmetry constructions. Actually, this rule produces twins, that is, links with same degree, Milnor number and homology H_3, with the exception of iterated Thom-Sebastiani sums of singularities of chain and cycle type, where the torsion and the Milnor number may vary. The Berglund-Hübsch transpose rule not only gives a framework to better understand the existence of SasakiEinstein twins but also gives a mechanism for producing new examples of Sasaki-Einstein twins in the rational homology 7 -sphere setting. We also give reasonable conditions for a Sasaki-Einstein rational homology 7-sphere to remain Sasaki-Einstein under the BH-transpose rule. In particular, we found 75 new examples of Sasaki-Einstein rational homology 7-spheres arising as links of not well-formed hypersurface singularities. |
| title | Beglund-Hübsch transpose and Sasaki-Einstein rational homology 7-spheres |
| topic | Differential Geometry 53C25, 57R60 |
| url | https://arxiv.org/abs/2311.15998 |