Paunescu, Laurentiu Invariants associated with blow-analytic homeomorphisms. (English) Zbl 1040.32025 Proc. Japan Acad., Ser. A 78, No. 10, 194-198 (2002). This is a very interesting paper on blow-analytic equisingularities. The author answers some fundamental questions on this topic raised by T-C.Kuo and P. D. Milman [in “Real analytic and algebraic singularities”, Pitman Res. Notes Math. Ser. 381, Longman, Harlow, 38–42 (1998; Zbl 0895.32004)]. Some easier proofs of some results of O. M. Abderrahmane [J. Math. Soc. Japan 54, No. 3, 513–550 (2002; Zbl 1031.58024)] are also given. Reviewer: D. Andrica (Cluj-Napoca) Cited in 2 Documents MSC: 32S15 Equisingularity (topological and analytic) 58K30 Global theory of singularities Keywords:blow-analytic equisingularities; arc-analytic Citations:Zbl 0895.32004; Zbl 1031.58024 PDF BibTeX XML Cite \textit{L. Paunescu}, Proc. Japan Acad., Ser. A 78, No. 10, 194--198 (2002; Zbl 1040.32025) Full Text: DOI OpenURL References: [1] Abderrahmane J, Ould M.: Polyèdre de Newton et trivialité en famille. J. Math. Soc. Japan, 54 , 513-550 (2002). · Zbl 1031.58024 [2] Bierstone, E., and Milman, P. D.: Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant. Invent. Math., 128 , 207-302 (1997). · Zbl 0896.14006 [3] Bierstone, E., and Milman, P. D.: Arc-analytic functions. Invent. Math., 101 , 411-424 (1990). · Zbl 0723.32005 [4] Fukui, T., Koike, S., and Kuo, T.-C.: Blow-analytic equisingularities, properties, problems and progress. Real Analytic and Algebraic Singularities. Pitman Res. Notes Math. ser. 381, Longman, Harlow, pp. 8-29 (1998). · Zbl 0954.26012 [5] Fukui, T., Kuo, T.-C., and Paunescu, L.: Constructing blow-analytic isomorphisms. Ann. Inst. Fourier (Grenoble), 51 (4), 1071-1084 (2001). · Zbl 0984.32005 [6] Hironaka, H.: Resolution of singularities of an algebraic variety over a field of characteristic zero, I. Ann. of Math. (2), 79 , 109-203 (1964); Resolution of singularities of an algebraic variety over a field of characteristic zero, II. Ann. of Math. (2), 79 , 205-326 (1964). · Zbl 0122.38603 [7] Hironaka, H.: Introduction to real-analytic sets and real-analytic maps. Quaderni dei Gruppi di Ricerca Matematica del Consiglio Nazionale delle Ricerche, Istituto Matematico “L. Tonelli” dell’Università di Pisa, Pisa (1973). · Zbl 0297.32008 [8] Kuo, T.-C.: The modified analytic trivialization of singularities. J. Math. Soc. Japan, 32 , 605-614 (1980). · Zbl 0509.58007 [9] Kuo, T.-C.: On classification of real singularities. Invent. Math., 82 , 257-262 (1985). · Zbl 0587.32018 [10] Kuo, T-C., and Milman, P. D.: On arc-analytic trivialisation of singularities. Real Analytic and Algebraic Singularities. Pitman Res. Notes Math. ser. 381, Longman, Harlow, pp. 38-42 (1998). · Zbl 0895.32004 [11] Kuo, T.-C., and Paunescu, L.: Equisingular Deformations in \(\CC^2\) and \(\RR^2\). (In preparation). [12] Kuo, T.-C., and Ward, J. N.: A Theorem on almost analytic equisingularity. J. Math. Soc. Japan, 33 , 471-484 (1981). · Zbl 0476.58004 [13] Kurdyka, K.: Ensembles semi-alaébriques symétriques par arcs. Math. Ann., 282 , 445-462 (1988). · Zbl 0686.14027 [14] Parusiński, A.: Subanalytic functions. Trans. Amer. Math. Soc., 344 (2), 583-595 (1994). · Zbl 0819.32006 [15] Paunescu, L.: A weighted version of the Kuiper-Kuo-Bochnak-Lojasiewicz theorem. J. Algebraic Geom., 2 (1), 69-79 (1993). · Zbl 0779.32003 [16] Paunescu, L.: An example of blow analytic homeomorphism. Real Analytic and Algebraic Singularities. Pitman Res. Notes Math. ser. 381, Longman, Harlow, pp. 62-63 (1998). · Zbl 0896.58012 [17] Paunescu, L.: An implicit function theorem for locally blow-analytic functions. Ann. Inst. Fourier (Grenoble), 51 (4), 1089-1100 (2001). · Zbl 0996.58008 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.