Limits of length functions of multi $p$-families of ideals
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916226785083392 |
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| author | Nguyen, Thai Thanh Pham, Vinh Anh |
| author_facet | Nguyen, Thai Thanh Pham, Vinh Anh |
| contents | We show the asymptotic relationship between the limit of the normalized length function of a multi-$p-$family of ideals and that of its shifted family under linear growth conditions in a local domain of characteristic $p$. Examples of multi-$p-$families of ideals including products of Frobenius powers of different ideals. We apply our results to obtain a generalized version of a formula due to Wantanabe-Yoshida for certain $p-$families using results from Verma, and to provide an instance of the existence of a mixed multiplicity version of multi-$p$-families of ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17712 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limits of length functions of multi $p$-families of ideals Nguyen, Thai Thanh Pham, Vinh Anh Commutative Algebra 13A18, 13D40, 13H15 We show the asymptotic relationship between the limit of the normalized length function of a multi-$p-$family of ideals and that of its shifted family under linear growth conditions in a local domain of characteristic $p$. Examples of multi-$p-$families of ideals including products of Frobenius powers of different ideals. We apply our results to obtain a generalized version of a formula due to Wantanabe-Yoshida for certain $p-$families using results from Verma, and to provide an instance of the existence of a mixed multiplicity version of multi-$p$-families of ideals. |
| title | Limits of length functions of multi $p$-families of ideals |
| topic | Commutative Algebra 13A18, 13D40, 13H15 |
| url | https://arxiv.org/abs/2404.17712 |