Resumen: In 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. Idioma: Inglés DOI: 10.1007/s10231-015-0546-3 Año: 2016 Publicado en: Annali di Matematica Pura ed Applicata 195, 5 (2016), 1749-1769 ISSN: 0373-3114 Factor impacto JCR: 0.864 (2016) Categ. JCR: MATHEMATICS rank: 84 / 310 = 0.271 (2016) - Q2 - T1 Categ. JCR: MATHEMATICS, APPLIED rank: 139 / 255 = 0.545 (2016) - Q3 - T2 Factor impacto SCIMAGO: 1.151 - Applied Mathematics (Q1)