On the degree of the singular subscheme of hypersurfaces in ${\mathbb P}^n$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866915975495942144 |
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| author | Dimca, Alexandru Sticlaru, Gabriel |
| author_facet | Dimca, Alexandru Sticlaru, Gabriel |
| contents | Explicit formulas determining the dimension and the degree of the singular subscheme of hypersurfaces in ${\mathbb P}^n$ are given in terms of the graded Betti numbers of the minimal free resolution of the corresponding Jacobian algebra. This gives in particular new restrictions which must be satisfied by such graded Betti numbers. We define a homologically strictly plus-one generated hypersurface, and show that such a hypersurface has a singular locus of dimension $n-2$ when its degree is not too low. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24308 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the degree of the singular subscheme of hypersurfaces in ${\mathbb P}^n$ Dimca, Alexandru Sticlaru, Gabriel Algebraic Geometry Commutative Algebra Explicit formulas determining the dimension and the degree of the singular subscheme of hypersurfaces in ${\mathbb P}^n$ are given in terms of the graded Betti numbers of the minimal free resolution of the corresponding Jacobian algebra. This gives in particular new restrictions which must be satisfied by such graded Betti numbers. We define a homologically strictly plus-one generated hypersurface, and show that such a hypersurface has a singular locus of dimension $n-2$ when its degree is not too low. |
| title | On the degree of the singular subscheme of hypersurfaces in ${\mathbb P}^n$ |
| topic | Algebraic Geometry Commutative Algebra |
| url | https://arxiv.org/abs/2604.24308 |