Constructing blow-analytic isomorphisms
[Construire des isomorphismes "blow-analytiques"]
Fukui, Toshizumi1 ; Kuo, Tzee-Char2 ; Paunescu, Laurentiu2
1 Saitama University, Fauclty of Science, Department of Mathematics, 255 Shimo-Okubo, Urawa 338 (Japon)
2 University of Sydney, School of Mathematics and Statistics, Sydney NSW 2006 (Australie)
Annales de l'Institut Fourier, Tome 51 (2001) no. 4, pp. 1071-1087.

Nous donnons des exemples d'isomorphismes "blow-analytiques" et via des modifications toriques, nous obtenons un théorème des fonctions inverses dans cette catégorie. Nous montrons aussi que on peut déformer toutes les courbes analytiques (via des isomorphismes rationnels "blow-analytiques") sur une courbe analytique lisse.

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

DOI : 10.5802/aif.1845
Classification : 32B20, 14Pxx
Keywords: blow-analytic, arc-analytic
Mot clés : blow-analytique, arc-analytique
Fukui, Toshizumi 1 ; Kuo, Tzee-Char 2 ; Paunescu, Laurentiu 2

1 Saitama University, Fauclty of Science, Department of Mathematics, 255 Shimo-Okubo, Urawa 338 (Japon)
2 University of Sydney, School of Mathematics and Statistics, Sydney NSW 2006 (Australie) 
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     title = {Constructing blow-analytic isomorphisms},
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     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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Fukui, Toshizumi; Kuo, Tzee-Char; Paunescu, Laurentiu. Constructing blow-analytic isomorphisms. Annales de l'Institut Fourier, Tome 51 (2001) no. 4, pp. 1071-1087. doi : 10.5802/aif.1845. http://www.numdam.org/articles/10.5802/aif.1845/

[1] V.I. Danilov The geometry of toric varieties, Russian Math. Surveys, Volume 33 (1978), pp. 97-154 | DOI | MR | Zbl

[2] A. du Plessis; T. Wall The geometry of topological stability, London Mathematical Society Monographs, New Series, 9, Oxford Science Publication, 1995 | MR | Zbl

[3] T. Fukui; S. Koike; T.-C. Kuo Blow-analytic equisingularities, properties, problems and progress, Real analytic and algebraic singularities (Pitman Research Notes in Mathematics Series), Volume 381 (1997), pp. 8-29 | Zbl

[4] H. Hironaka Resolution of Singularities of an algebraic variety over a field of characteristic zero, I-II, Ann. of Math., Volume 97 (1964) | MR | Zbl

[5] M. Kobayashi; T.-C. Kuo On Blow-analytic equivalence of embedded curve singularities, Real analytic and algebraic singularities (Pitman Research Notes in Mathematics Series), Volume 381 (1997), pp. 30-37 | Zbl

[6] T.-C. Kuo Generalized Newton - Puiseux Theory and Hensel's Lemma in ℂ[[x,y]], Can. J. Math., Volume XLI (1989) no. 6, pp. 1101-1116 | MR | Zbl

[7] T.-C. Kuo A Simple Algorithm For Deciding Primes In 𝕂[[x,y]], Can. J. Math., Volume 47 (1995) no. 4, pp. 801-816 | DOI | MR | Zbl

[8] T.-C. Kuo The modified analytic trivialization of singularities, J. Math. Soc. Japan, Volume 32 (1980), pp. 605-614 | DOI | MR | Zbl

[9] T.-C. Kuo On classification of real singularities, Invent. Math., Volume 82 (1985), pp. 257-262 | DOI | MR | Zbl

[10] T.-C. Kuo; J. N. Ward A Theorem on almost analytic equisingularity, J. Math. Soc. Japan, Volume 33 (1981), pp. 471-484 | DOI | MR | Zbl

[11] T. Oda Convex bodies and algebraic geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3, Folge Band, 14, Springer-Verlag, 1987 | EuDML | MR | Zbl

[12] L. Paunescu An example of blow-analytic homeomorphism, Real analytic and algebraic singularities (Pitman Research Notes in Mathematics Series), Volume 381 (1997), pp. 62-63 | Zbl

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