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Toshizumi Fukui; Tzee-Char Kuo; Laurentiu Paunescu
Constructing blow-analytic isomorphisms
(Construire des isomorphismes "blow-analytiques")
Annales de l'institut Fourier, 51 no. 4 (2001), p. 1071-1087, doi: 10.5802/aif.1845
Article PDF | Reviews MR 1849215 | Zbl 0984.32005
Class. Math.: 32B20, 14Pxx
Keywords: blow-analytic, arc-analytic

Résumé - Abstract

In this paper we construct non-trivial examples of {\it blow-analytic} isomorphisms and we obtain, via toric modifications, an inverse function theorem in this category. We also show that any analytic curve in ${\Bbb R}^n, n\ge 3$, can be deformed via a rational blow- analytic isomorphism of ${\Bbb R}^n$, to a smooth analytic arc.

Bibliography

[1] V.I. Danilov, “The geometry of toric varieties”, Russian Math. Surveys 33 (1978), p. 97-154 Article |  MR 495499 |  Zbl 0425.14013
[2] A. du Plessis & T. Wall, The geometry of topological stability, London Mathematical Society Monographs, New Series 9, Oxford Science Publication, 1995  MR 1408432 |  Zbl 0870.57001
[3] T. Fukui, S. Koike & T.-C. Kuo, Blow-analytic equisingularities, properties, problems and progress, Pitman Research Notes in Mathematics Series, Longman, 1997, p. 8-29  Zbl 0954.26012
[4] H. Hironaka, “Resolution of Singularities of an algebraic variety over a field of characteristic zero, I-II”, Ann. of Math. 97 (1964)  MR 199184 |  Zbl 0122.38603
[5] M. Kobayashi & T.-C. Kuo, On Blow-analytic equivalence of embedded curve singularities, Pitman Research Notes in Mathematics Series, Longman, 1997, p. 30-37  Zbl 0899.32002
[6] T.-C. Kuo, “Generalized Newton - Puiseux Theory and Hensel's Lemma in ${\Bbb C}[[x,y]]$”, Can. J. Math. XLI (1989) no. 6, p. 1101-1116  MR 1018453 |  Zbl 0716.13015
[7] T.-C. Kuo, “A Simple Algorithm For Deciding Primes In ${\Bbb K}[[x,y]]$”, Can. J. Math. 47 (1995) no. 4, p. 801-816 Article |  MR 1346164 |  Zbl 0857.13019
[8] T.-C. Kuo, “The modified analytic trivialization of singularities”, J. Math. Soc. Japan 32 (1980), p. 605-614 Article |  MR 589100 |  Zbl 0509.58007
[9] T.-C. Kuo, “On classification of real singularities”, Invent. Math. 82 (1985), p. 257-262 Article |  MR 809714 |  Zbl 0587.32018
[10] T.-C. Kuo & J. N. Ward, “A Theorem on almost analytic equisingularity”, J. Math. Soc. Japan 33 (1981), p. 471-484 Article |  MR 620284 |  Zbl 0476.58004
[11] T. Oda, Convex bodies and algebraic geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete 3, Folge Band, 14, Springer-Verlag, 1987  MR 922894 |  Zbl 0628.52002
[12] L. Paunescu, An example of blow-analytic homeomorphism, Pitman Research Notes in Mathematics Series, Longman, 1997, p. 62-63  Zbl 0896.58012
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