Limits of length functions of multi -families of ideals
arXiv:2404.17712
Abstract
We show the asymptotic relationship between the limit of the normalized length function of a multi-family of ideals and that of its shifted family under linear growth conditions in a local domain of characteristic . Examples of multi-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 families using results from Verma, and to provide an instance of the existence of a mixed multiplicity version of multi--families of ideals.
22 pages