doi:10.1007/s10231-015-0546-3engMartín-Morales, J.Semistable reduction of a normal crossing Q -divisorART-2016-96345In a previous work, we have introduced the notion of embedded Q-resolution, which allows the final ambient space to contain abelian quotient singularities, and A’Campo’s formula was calculated in this setting. Here, we study the semistable reduction associated with an embedded Q-resolution and compute the mixed Hodge structure on the cohomology of the Milnor fiber in the isolated case using a generalization of Steenbrink’s spectral sequence. Examples of Yomdin-Lê surface singularities are presented as an application.2016http://zaguan.unizar.es/record/13174210.1007/s10231-015-0546-3http://zaguan.unizar.es/record/131742oai:zaguan.unizar.es:131742info:eu-repo/grantAgreement/ES/DGA/E15info:eu-repo/grantAgreement/ES/MICINN/MTM2013-45710-C2-1-PAnnali di Matematica Pura ed Applicata 195, 5 (2016), 1749-1769All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess