Complex analysis and geometry
On some properties of the Łojasiewicz exponent
Comptes Rendus. Mathématique, Volume 359 (2021) no. 8, pp. 991-997.

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

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Published online:
DOI: 10.5802/crmath.238
Eyral, Christophe 1; Mostowski, Tadeusz 2; Pragacz, Piotr 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.
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Eyral, Christophe; Mostowski, Tadeusz; Pragacz, Piotr. On some properties of the Łojasiewicz exponent. Comptes Rendus. Mathématique, Volume 359 (2021) no. 8, pp. 991-997. doi : 10.5802/crmath.238. http://www.numdam.org/articles/10.5802/crmath.238/

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

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

[3] Domitrz, Wojciech; Mormul, Piotr; Pragacz, Piotr 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] Jensen, Gary R. Higher order contact of submanifolds of homogeneous spaces, Lecture Notes in Mathematics, 610, Springer, 1977 | MR | Zbl

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

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

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

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

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

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

[11] Parusiński, Adam 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 (Uhlenbeck, Karen, ed.), Publish or Perish Inc., Houston, 1993, pp. 73-89 | Zbl

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

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

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

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