Rational symbolic powers of ideals
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912895522045952 |
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| author | Dey, Souvik Ha, Tai Huy Mahato, Dipendranath Mantero, Paolo |
| author_facet | Dey, Souvik Ha, Tai Huy Mahato, Dipendranath Mantero, Paolo |
| contents | We introduce and study rational symbolic powers of ideals in Noetherian rings. We give membership criteria for rational symbolic powers and discuss settings where they agree with integer symbolic powers. We investigate the binomial expansion formula for rational symbolic powers of mixed sums of ideals. Finally, we study rational symbolic powers of monomial ideals. In this case, we give a convex-geometric description of the rational symbolic powers. We also show that the filtration of rational symbolic powers of a monomial ideal is asymptotically stable and, as a consequence, deduce that the asymptotic regularity and asymptotic depth for this filtration exist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02732 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rational symbolic powers of ideals Dey, Souvik Ha, Tai Huy Mahato, Dipendranath Mantero, Paolo Commutative Algebra 13C05, 13A15, 13D45 We introduce and study rational symbolic powers of ideals in Noetherian rings. We give membership criteria for rational symbolic powers and discuss settings where they agree with integer symbolic powers. We investigate the binomial expansion formula for rational symbolic powers of mixed sums of ideals. Finally, we study rational symbolic powers of monomial ideals. In this case, we give a convex-geometric description of the rational symbolic powers. We also show that the filtration of rational symbolic powers of a monomial ideal is asymptotically stable and, as a consequence, deduce that the asymptotic regularity and asymptotic depth for this filtration exist. |
| title | Rational symbolic powers of ideals |
| topic | Commutative Algebra 13C05, 13A15, 13D45 |
| url | https://arxiv.org/abs/2511.02732 |