Beglund-H\'ubsch transpose and Sasaki-Einstein rational homology 7-spheres
| Autor: | Valle, Jaime Cuadros, Gomez, Ralph R., Vicente, Joe Lope |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Communications in Mathematical Physics Volume 405, article number 199, (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00220-024-05093-5 |
| Popis: | We show that links of invertible polynomials coming from the Johnson and Koll\'ar list of K\"ahler-Einstein 3-folds that are rational homology 7-spheres remain rational homology 7-spheres under the so-called Berglund-H\"ubsch 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-H\"ubsch 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. Comment: We have changed the title, corrected minor typos and added Remark 4.2 |
| Databáze: | arXiv |
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