2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131933We study the multi-dimensional persistence of Carlsson and Zomorodian and obtain a finer classification based upon the higher tor-modules of a persistence module. We propose a variety structure on the set of isomorphism classes of these modules, and present several examples. We also provide a geometric interpretation for the higher tor-modules of homology modules of multi-filtered simplicial complexes.21 pages, 4 figuresAlgebraic Topologytext