Herzog ideals and $F$-singularities
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909986624372736 |
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| author | De Stefani, Alessandro Ma, Linquan Varbaro, Matteo |
| author_facet | De Stefani, Alessandro Ma, Linquan Varbaro, Matteo |
| contents | In this paper we study the connection between Herzog ideals (i.e., ideals with a squarefree Gröbner degeneration) and $F$-singularities. More precisely, we show that, in positive characteristic, homogeneous Herzog ideals define $F$-anti-nilpotent rings, and we inquire, in characteristic 0, on a surprising relationship between being Herzog ideals after a change of coordinates and defining rings of dense open $F$-pure type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06476 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Herzog ideals and $F$-singularities De Stefani, Alessandro Ma, Linquan Varbaro, Matteo Commutative Algebra Algebraic Geometry In this paper we study the connection between Herzog ideals (i.e., ideals with a squarefree Gröbner degeneration) and $F$-singularities. More precisely, we show that, in positive characteristic, homogeneous Herzog ideals define $F$-anti-nilpotent rings, and we inquire, in characteristic 0, on a surprising relationship between being Herzog ideals after a change of coordinates and defining rings of dense open $F$-pure type. |
| title | Herzog ideals and $F$-singularities |
| topic | Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/2601.06476 |