Asymptotic colengths for families of ideals: an analytic approach
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916440583438336 |
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| author | Das, Sudipta Meng, Cheng |
| author_facet | Das, Sudipta Meng, Cheng |
| contents | This article focuses on the existence of asymptotic colengths for families of $\fm_{R}$-primary ideals in a Noetherian local ring $(R,\fm)$. In any characteristic, we generalize graded families to weakly graded families of ideals, and in prime characteristic, we explore various families such as weakly $p$-families and weakly inverse $p$-families. The main contribution of this paper is providing a unified analytic method to prove the existence of limits. Additionally, we establish Brunn-Minkowski type inequalities, positivity results, and volume = multiplicity formulas for these families of ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11991 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic colengths for families of ideals: an analytic approach Das, Sudipta Meng, Cheng Commutative Algebra This article focuses on the existence of asymptotic colengths for families of $\fm_{R}$-primary ideals in a Noetherian local ring $(R,\fm)$. In any characteristic, we generalize graded families to weakly graded families of ideals, and in prime characteristic, we explore various families such as weakly $p$-families and weakly inverse $p$-families. The main contribution of this paper is providing a unified analytic method to prove the existence of limits. Additionally, we establish Brunn-Minkowski type inequalities, positivity results, and volume = multiplicity formulas for these families of ideals. |
| title | Asymptotic colengths for families of ideals: an analytic approach |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2410.11991 |