Constructing blow-analytic isomorphisms

Toshizumi Fukui[1]; Tzee-Char Kuo[2]; Laurentiu Paunescu[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)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 4, page 1071-1087
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Fukui, Toshizumi, Kuo, Tzee-Char, and Paunescu, Laurentiu. "Constructing blow-analytic isomorphisms." Annales de l’institut Fourier 51.4 (2001): 1071-1087. <http://eudml.org/doc/115934>.

@article{Fukui2001,
abstract = {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 $\{\mathbb \{R\}\}^n, n\ge 3$, can be deformed via a rational blow- analytic isomorphism of $\{\mathbb \{R\}\}^n$, to a smooth analytic arc.},
affiliation = {Saitama University, Fauclty of Science, Department of Mathematics, 255 Shimo-Okubo, Urawa 338 (Japon); University of Sydney, School of Mathematics and Statistics, Sydney NSW 2006 (Australie); University of Sydney, School of Mathematics and Statistics, Sydney NSW 2006 (Australie)},
author = {Fukui, Toshizumi, Kuo, Tzee-Char, Paunescu, Laurentiu},
journal = {Annales de l’institut Fourier},
keywords = {blow-analytic; arc-analytic; real analytic singularities; blow-analytic homeomorphisms},
language = {eng},
number = {4},
pages = {1071-1087},
publisher = {Association des Annales de l'Institut Fourier},
title = {Constructing blow-analytic isomorphisms},
url = {http://eudml.org/doc/115934},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Fukui, Toshizumi
AU - Kuo, Tzee-Char
AU - Paunescu, Laurentiu
TI - Constructing blow-analytic isomorphisms
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 4
SP - 1071
EP - 1087
AB - 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 ${\mathbb {R}}^n, n\ge 3$, can be deformed via a rational blow- analytic isomorphism of ${\mathbb {R}}^n$, to a smooth analytic arc.
LA - eng
KW - blow-analytic; arc-analytic; real analytic singularities; blow-analytic homeomorphisms
UR - http://eudml.org/doc/115934
ER -

References

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  2. A. du Plessis, T. Wall, The geometry of topological stability, 9 (1995), Oxford Science Publication Zbl0870.57001MR1408432
  3. T. Fukui, S. Koike, T.-C. Kuo, Blow-analytic equisingularities, properties, problems and progress, Real analytic and algebraic singularities 381 (1997), 8-29, Longman Zbl0954.26012
  4. H. Hironaka, Resolution of Singularities of an algebraic variety over a field of characteristic zero, I-II, Ann. of Math. 97 (1964) Zbl0122.38603MR199184
  5. M. Kobayashi, T.-C. Kuo, On Blow-analytic equivalence of embedded curve singularities, Real analytic and algebraic singularities 381 (1997), 30-37, Longman Zbl0899.32002
  6. T.-C. Kuo, Generalized Newton - Puiseux Theory and Hensel’s Lemma in ℂ [ [ x , y ] ] , Can. J. Math. XLI (1989), 1101-1116 Zbl0716.13015MR1018453
  7. T.-C. Kuo, A Simple Algorithm For Deciding Primes In 𝕂 [ [ x , y ] ] , Can. J. Math. 47 (1995), 801-816 Zbl0857.13019MR1346164
  8. T.-C. Kuo, The modified analytic trivialization of singularities, J. Math. Soc. Japan 32 (1980), 605-614 Zbl0509.58007MR589100
  9. T.-C. Kuo, On classification of real singularities, Invent. Math. 82 (1985), 257-262 Zbl0587.32018MR809714
  10. T.-C. Kuo, J. N. Ward, A Theorem on almost analytic equisingularity, J. Math. Soc. Japan 33 (1981), 471-484 Zbl0476.58004MR620284
  11. T. Oda, Convex bodies and algebraic geometry, 3, Folge Band, 14 (1987), Springer-Verlag Zbl0628.52002MR922894
  12. L. Paunescu, An example of blow-analytic homeomorphism, Real analytic and algebraic singularities 381 (1997), 62-63, Longman Zbl0896.58012

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