Hypergeometric Discriminants
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911057119805440 |
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| author | Matsubara-Heo, Saiei-Jaeyeong |
| author_facet | Matsubara-Heo, Saiei-Jaeyeong |
| contents | Given a family of varieties, the Euler discriminant locus distinguishes points where Euler characteristic differs from its generic value. We introduce a hypergeometric system associated with a flat family of very affine locally complete intersection varieties. It is proven that the Euler discriminant locus is its singular locus and is purely one-codimensional unless it is empty. Of particular interest is a family of very affine hypersurfaces. We coin the term hypergeometric discriminant for the characteristic cycle of the hypergeometric system and establish a formula in terms of likelihood equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13163 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hypergeometric Discriminants Matsubara-Heo, Saiei-Jaeyeong Algebraic Geometry High Energy Physics - Theory Given a family of varieties, the Euler discriminant locus distinguishes points where Euler characteristic differs from its generic value. We introduce a hypergeometric system associated with a flat family of very affine locally complete intersection varieties. It is proven that the Euler discriminant locus is its singular locus and is purely one-codimensional unless it is empty. Of particular interest is a family of very affine hypersurfaces. We coin the term hypergeometric discriminant for the characteristic cycle of the hypergeometric system and establish a formula in terms of likelihood equations. |
| title | Hypergeometric Discriminants |
| topic | Algebraic Geometry High Energy Physics - Theory |
| url | https://arxiv.org/abs/2505.13163 |