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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2508.15497 |
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| _version_ | 1866908857732694016 |
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| author | Balnojan, Sven Hertling, Claus |
| author_facet | Balnojan, Sven Hertling, Claus |
| contents | Isolated hypersurface singularities come equipped with distinguished bases of their Milnor lattices and with upper triangular integral matrices, which are called here distinguished matrices. These matrices form an orbit of a braid group and a sign change group. This paper proposes to characterize the distinguished matrices of singularities within all upper triangular integral matrices in terms of the variance of certain spectral numbers. It succeeds in the positive definite and the positive semidefinite cases. The ADE root lattices are crucial. In the semidefinite cases, results on non-reduced presentations of Weyl group elements are used. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15497 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterization of distinguished matrices of isolated hypersurface singularities through their spectral numbers Balnojan, Sven Hertling, Claus Algebraic Geometry Representation Theory 32S25, 17B22, 06B15, 20F36, 20F55 Isolated hypersurface singularities come equipped with distinguished bases of their Milnor lattices and with upper triangular integral matrices, which are called here distinguished matrices. These matrices form an orbit of a braid group and a sign change group. This paper proposes to characterize the distinguished matrices of singularities within all upper triangular integral matrices in terms of the variance of certain spectral numbers. It succeeds in the positive definite and the positive semidefinite cases. The ADE root lattices are crucial. In the semidefinite cases, results on non-reduced presentations of Weyl group elements are used. |
| title | Characterization of distinguished matrices of isolated hypersurface singularities through their spectral numbers |
| topic | Algebraic Geometry Representation Theory 32S25, 17B22, 06B15, 20F36, 20F55 |
| url | https://arxiv.org/abs/2508.15497 |