Limits of length functions of multi $p$-families of ideals

Thai Thanh Nguyen; Vinh Anh Pham

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arXiv · 2404.17712

Limits of length functions of multi $p$-families of ideals

Thai Thanh Nguyen·Vinh Anh Pham

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Abstract

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.

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Thai Thanh Nguyen, Vinh Anh Pham. 2024-04-26. Limits of length functions of multi $p$-families of ideals. https://arxiv.org/abs/2404.17712

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