Hauser, Herwig; Müller, Gerd The cancellation property for direct products of analytic space germs. (English) Zbl 0702.32008 Math. Ann. 286, No. 1-3, 209-223 (1990). The authors prove the cancellation property for germs of analytic spaces. Namely if X,Y and Z are germs of analytic spaces and \(X\times Z\to^{\sim}Y\times Z\), then \(X\to^{\sim}Y\). The key theorem is “Unique factorization property of algebroid spaces” and as an application, they obtain the above theorem. Reviewer: T.Akahori Cited in 1 ReviewCited in 3 Documents MSC: 32B10 Germs of analytic sets, local parametrization Keywords:cancellation property; germs of analytic spaces PDFBibTeX XMLCite \textit{H. Hauser} and \textit{G. Müller}, Math. Ann. 286, No. 1--3, 209--223 (1990; Zbl 0702.32008) Full Text: DOI EuDML References: [1] Artin, M.: On the solutions of analytic equations. Invent. Math.5, 277-291 (1968) · Zbl 0172.05301 [2] Artin, M.: Algebraic spaces. New Haven London: Yale University Press 1971 · Zbl 0226.14001 [3] Beauville, A., Colliot-Thélène, J.-L., Sansuc, J.-J., Swinnerton-Dyer, P.: Variétés stablement rationelles non rationelles. Ann. Math.121, 283-318 (1985) · Zbl 0589.14042 [4] Becker, J., Denef, J., Lipshitz, L.: The approximation property for some 5-dimensional Henselian rings. Trans. Am. Math. Soc.276, 301-309 (1983) · Zbl 0531.14004 [5] Bierstone, E., Milman, P.: Relations among analytic functions. II. Ann. Inst. Fourier37, 49-77 (1987) · Zbl 0611.32003 [6] Ephraim, R.: Isosingular loci and the cartesian product structure of complex analytic singularities. Trans. Am. Math. Soc.241, 357-371 (1978) · Zbl 0395.32006 [7] Ephraim, R.:C ? and analytic equivalence of singularities. Rice Univ. Stud.59, 11-32 (1973) · Zbl 0277.32021 [8] Fischer, G.: Complex analytic geometry (Lect. Notes Math., Vol. 538) Berlin Heidelberg New York: Springer 1976 · Zbl 0343.32002 [9] Gabriélov, A.M.: Formal relations between analytic functions. Funct. Anal. Appl.5, 318-319 (1971) · Zbl 0254.32009 [10] Gaffney, T., Hauser, H.: Characterizing singularities of varieties and of mappings. Invent. Math.81, 427-447 (1985) · Zbl 0627.14004 [11] Horst, C.: On product decompositions of complex spaces. Habilitationsschrift, Universität München · Zbl 0790.32010 [12] Horst, C.: Decomposition of compact complex varieties and the cancellation problem. Math. Ann.271, 467-477 (1985) · Zbl 0556.32001 [13] Horst, C.: A cancellation theorem for Artinian local algebras. Math. Ann.276, 657-662 (1987) · Zbl 0595.13007 [14] Hauser, H., Müller, G.: Analytic curves in power series rings. Compos. Math. (to appear) · Zbl 0721.32003 [15] Kambayashi, T.: On Fujita’s strong cancellation theorem for the affine plane. J. Fac. Sci. Univ. Tokyo, Sect. I A Math.27, 535-548 (1980) · Zbl 0453.14015 [16] Lazzeri, F., Tognoli, A.: Alcune proprietà degli spazi algebrici. Ann. Sc. Norm. Super. Pisa Cl. Sci., III. Ser.24, 597-632 (1970) · Zbl 0205.25201 [17] Parigi, G.: Caractérisation des variétés compactes simplifiables et applications aux surfaces algébriques. Math. Z.190, 371-378 (1985) · Zbl 0589.32047 [18] Popescu, D.: General Néron desingularization and approximation. Nagoya Math. J.104, 85-115 (1986) · Zbl 0592.14014 [19] Rotthaus, C.: On the approximation property for excellent rings. Invent. Math.88, 39-63 (1987) · Zbl 0614.13014 [20] Spallek, K.: Produktzerlegung und Äquivalenz von Raumkeimen I. In: C. Andreian Cazacu et al. (eds.) Complex analysis Fifth Romanian-Finnish Seminar Part 2. Proceedings, Bucharest 1981 (Lect. Notes Math., Vol. 1014, pp. 78-100). Berlin Heidelberg New York: Springer 1983 [21] Zariski, O.: Studies in equisingularity. I. Equivalent singularities of plane algebroid curves. Am. J. Math.87, 507-536 (1965) · Zbl 0132.41601 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.