# Revista Matemática Iberoamericana

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**Volume 29, Issue 3, 2013, pp. 939–967**

**DOI: 10.4171/RMI/745**

Published online: 2013-08-04

Monodromy zeta function formula for embedded $\mathbf{Q}$-resolutions

Jorge Martín-Morales^{[1]}(1) Academia General Militar, Zaragoza, Spain

In previous work we have introduced the notion of an embedded $\mathbf{Q}$-resolution, which essentially consists in allowing the final ambient space to contain abelian quotient singularities. Here we give a generalization to this setting of N. A’Campo’s formula for the monodromy zeta function of a singularity. Some examples of its application are shown.

*Keywords: *Quotient singularity, weighted blow-up, embedded $\mathbf{Q}$-resolution, monodromy zeta function

Martín-Morales Jorge: Monodromy zeta function formula for embedded $\mathbf{Q}$-resolutions. *Rev. Mat. Iberoam.* 29 (2013), 939-967. doi: 10.4171/RMI/745