Martín-Morales, Jorge Monodromy zeta function formula for embedded \(\mathbf{Q}\)-resolutions. (English) Zbl 1276.32023 Rev. Mat. Iberoam. 29, No. 3, 939-967 (2013). Summary: 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. Cited in 13 Documents MSC: 32S45 Modifications; resolution of singularities (complex-analytic aspects) 32S25 Complex surface and hypersurface singularities 32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) Keywords:quotient singularity; weighted blow-up; embedded \(\mathbf{Q}\)-resolution; monodromy zeta function PDFBibTeX XMLCite \textit{J. Martín-Morales}, Rev. Mat. Iberoam. 29, No. 3, 939--967 (2013; Zbl 1276.32023) Full Text: DOI arXiv References: [1] A’Campo, N.: La fonction z\hat eta d’une monodromie. Comment. Math. Helv. 50 (1975), 233-248. · Zbl 0333.14008 · doi:10.1007/BF02565748 [2] Artal Bartolo, E., Martín-Morales, J. and Ortigas-Galindo, J.: Cartier and Weil divisors on varieties with quotient singularities. Available at arXiv, 1104.5628v1 [math.AG]. · Zbl 1314.32042 [3] Artal Bartolo, E., Martín-Morales, J. and Ortigas-Galindo, J.: Intersec- tion theory on abelian-quotient V -surfaces and Q-resolutions. Available at arXiv, 1105.1321v1 [math.AG]. [4] Artal Bartolo, E.: Forme de Jordan de la monodromie des singularités su- perisolées de surfaces. Mem. Amer. Math. Soc. 109 (1994), no. 525, x+84 pp. [5] Baily, W. L. Jr.: The decomposition theorem for V -manifolds. Amer. J. Math. 78 (1956), 862-888. [5] Dimca, A.: Sheaves in topology. Universitext, Springer-Verlag, Berlin, 2004. · Zbl 1043.14003 [6] Dolgachev, I.: Weighted projective varieties. In Group actions and vector fields (Vancouver, BC, 1981), 34-71. Lecture Notes in Math. 956, Springer, Berlin, 1982. · Zbl 0516.14014 [7] Fujiki, A.: On resolutions of cyclic quotient singularities. Publ. Res. Inst. Math. Sci. 10 (1974/75), no. 1, 293-328. · Zbl 0313.32012 · doi:10.2977/prims/1195192183 [8] Gusein-Zade, S. M., Luengo, I. and Melle, A.: Partial resolutions and the zeta- function of a singularity. Comment. Math. Helv. 72 (1997), no. 2, 244-256. · Zbl 0901.32024 · doi:10.1007/s000140050014 [9] Hirzebruch, F., Neumann, W. D. and Koh, S. S.: Differentiable manifolds and quadratic forms. Appendix II by W. Scharlau. Lecture Notes in Pure and Applied Mathematics 4, Marcel Dekker, New York, 1971. · Zbl 0226.57001 [10] Kollár, J. and Mori, S.: Birational geometry of algebraic varieties. Cambridge Tracts in Mathematics 134, Cambridge University Press, Cambridge, 1998. · Zbl 0926.14003 [11] Luengo, I.: The \mu -constant stratum is not smooth. Invent. Math. 90 (1987), no. 1, 139-152. · Zbl 0627.32018 · doi:10.1007/BF01389034 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.