Quadratic linear strands of prime ideals
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909029963399168 |
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| author | Caviglia, Giulio De Stefani, Alessandro |
| author_facet | Caviglia, Giulio De Stefani, Alessandro |
| contents | We prove sharp estimates on the quadratic strand of the resolution of any homogeneous prime ideal in a standard graded polynomial ring over an arbitrary field. Our bounds only depend on the height of the prime ideal, and they are optimal since for every $h \geq 1$ we show that there exists a prime ideal of height $h$ achieving them. In particular, we show that a prime ideal of height $h$ can contain at most $h^2$ quadratic minimal generators, and that there exists a prime ideal minimally generated by $h^2$ quadrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09143 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quadratic linear strands of prime ideals Caviglia, Giulio De Stefani, Alessandro Commutative Algebra We prove sharp estimates on the quadratic strand of the resolution of any homogeneous prime ideal in a standard graded polynomial ring over an arbitrary field. Our bounds only depend on the height of the prime ideal, and they are optimal since for every $h \geq 1$ we show that there exists a prime ideal of height $h$ achieving them. In particular, we show that a prime ideal of height $h$ can contain at most $h^2$ quadratic minimal generators, and that there exists a prime ideal minimally generated by $h^2$ quadrics. |
| title | Quadratic linear strands of prime ideals |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2605.09143 |