On some properties of the Łojasiewicz exponent

Christophe Eyral; Tadeusz Mostowski; Piotr Pragacz

doi:10.5802/crmath.238

Complex analysis and geometry

On some properties of the Łojasiewicz exponent

Christophe Eyral ¹ ; Tadeusz Mostowski ²; Piotr Pragacz ¹

¹ Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland.
² Department of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland.

Comptes Rendus. Mathématique, Volume 359 (2021) no. 8, pp. 991-997.

Abstract

In this note, we investigate the behaviour of the Łojasiewicz exponent under hyperplane sections and its relation to the order of tangency.

Received: 2020-05-18
Revised: 2021-01-18
Accepted: 2021-06-13
Published online: 2021-10-08

DOI: 10.5802/crmath.238

Author's affiliations:

Christophe Eyral ¹; Tadeusz Mostowski ²; Piotr Pragacz ¹

¹ Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland.
² Department of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland.

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Christophe Eyral and Tadeusz Mostowski and Piotr Pragacz},
     title = {On some properties of the {{\L}ojasiewicz} exponent},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {991--997},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {8},
     year = {2021},
     doi = {10.5802/crmath.238},
     language = {en},
}

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Christophe Eyral; Tadeusz Mostowski; Piotr Pragacz. On some properties of the Łojasiewicz exponent. Comptes Rendus. Mathématique, Volume 359 (2021) no. 8, pp. 991-997. doi : 10.5802/crmath.238. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.238/

References
Cited by

[1] Ewa Cygan; Piotr Tworzewski Proper intersection multiplicity and regular separation of analytic sets, Ann. Pol. Math., Volume 59 (1994) no. 3, pp. 293-298 | DOI | MR | Zbl

[2] Maciej P. Denkowski Regular separation with parameter of complex analytic sets, Kodai Math. J., Volume 30 (2007) no. 3, pp. 429-437 | MR | Zbl

[3] Wojciech Domitrz; Piotr Mormul; Piotr Pragacz Order of tangency between manifolds, Schubert Calculus and its applications in combinatorics and representation theory (Springer Monographs in Mathematics), Volume 332, Springer, 2020, pp. 27-42 | DOI | MR | Zbl

[4] Gary R. Jensen Higher order contact of submanifolds of homogeneous spaces, Lecture Notes in Mathematics, 610, Springer, 1977 | MR | Zbl

[5] Stanis Łojasiewicz Ensembles semi-analytiques, I.H.E.S, Bures-sur-Yvette, 1965 (https://perso.univ-rennes1.fr/michel.coste/Lojasiewicz.pdf)

[6] Stanis Łojasiewicz On semi-analytic and subanalytic geometry, Panoramas of mathematics (Warsaw, 1992/1994) (Bronisław Jakubczyk, ed.) (Banach Center Publications), Volume 34, Polish Academy of Sciences, 1995, pp. 89-104 | MR | Zbl

[7] Tadeusz Mostowski Lipschitz equisingularity, Diss. Math., Volume 243 (1985) | MR | Zbl

[8] Nhan Nguyen; Guillaume Valette Lipschitz stratifications in o-minimal structures, Ann. Sci. Éc. Norm. Supér., Volume 49 (2016) no. 2, pp. 399-421 | DOI | MR | Zbl

[9] Adam Parusiński Lipschitz properties of semi-analytic sets, Ann. Inst. Fourier, Volume 38 (1988) no. 4, pp. 189-213 | DOI | Numdam | MR | Zbl

[10] Adam Parusiński Lipschitz stratification of real analytic sets, Singularities (Warsaw, 1985) (Banach Center Publications), Volume 20, PWN, Warsaw, 1988, pp. 323-333 | MR | Zbl

[11] Adam Parusiński Lipschitz stratification, Global analysis in modern mathematics, Proceedings of the symposium in honor of Richard Palais’ sixtieth birthday, University of Maine, Orono, ME, USA, August 8–10, 1991, and at Brandeis University, Waltham, MA, USA, August 12, 1992 (Karen Uhlenbeck, ed.), Publish or Perish Inc., Houston, 1993, pp. 73-89 | Zbl

[12] Adam Parusiński Lipschitz stratification of subanalytic sets, Ann. Sci. Éc. Norm. Supér., Volume 27 (1994) no. 6, pp. 661-696 | DOI | Numdam | MR | Zbl

[13] Klaus Scharnhorst Angles in complex vector spaces, Acta Appl. Math., Volume 69 (2001) no. 1, pp. 95-103 | DOI | MR | Zbl

[14] Stanisław Spodzieja The Łojasiewicz exponent of subanalytic sets, Ann. Pol. Math., Volume 87 (2005), pp. 247-263 | DOI | MR | Zbl

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