Differential invariance of the multiplicity of real and complex analytic sets

• Autores: Jose Edson Sampaio
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 66, Nº 1, 2022, págs. 355-368
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper is devoted to proving the differential invariance of the multiplicity of real and complex analytic sets. In particular, we prove the real version of the Gau–Lipman theorem, i.e., it is proved that the multiplicity mod 2 of real analytic sets is a differential invariant. We also prove a generalization of the Gau–Lipmantheorem.

• Referencias bibliográficas
  • E. M. Chirka, “Complex Analytic Sets”, Translated from the Russian by R. A. M. Hoksbergen, Mathematics and its Applications (Soviet Series)...
  • G. Comte, Équisingularité réelle: nombres de Lelong et images polaires, Ann.Sci. Éc. Norm. Supér. (4) ´ 33(6) (2000), 757–788. DOI: 10.1016/s0012-9593(00)01052-1.
  • R. Ephraim, C1 preservation of multiplicity, Duke Math. 43(4) (1976), 797–803. DOI: 10.1215/S0012-7094-76-04361-1.
  • R. Ephraim, The cartesian product structure and C∞ equivalences of singularities, Trans. Amer. Math. Soc. 224(2) (1976), 299–311. DOI: /10.2307/1997477.
  • T. Fukui, K. Kurdyka, and L. Paunescu, An inverse mapping theorem for arcanalytic homeomorphisms, in: “Geometric Singularity Theory”, Banach...
  • Y.-N. Gau and J. Lipman, Differential invariance of multiplicity on analytic varieties, Inventiones mathematicae 73(2) (1983), 165–188. DOI:...
  • K. Kurdyka and G. Raby, Densit´e des ensembles sous-analytiques, Ann. Inst. Fourier (Grenoble) 39(3) (1989), 753–771. DOI: 10.5802/aif.1186.
  • R. Narasimhan, “Introduction to the Theory of Analytic Spaces”, Lecture Notes in Mathematics 25, Springer-Verlag, Berlin, Heidelberg, 1966....
  • W. Pawlucki, Quasi-regular boundary and Stokes’ formula for a sub-analytic leaf, in: “Seminar on Deformations” ( Lawrynowicz J. (eds)), Lecture...
  • J.-J. Risler, Invariant curves and topological invariants for real plane analytic vector fields, J. Differential Equations 172(1) (2001),...
  • J. E. Sampaio, A proof of the differentiable invariance of the multiplicity using spherical blowing-up, Rev. R. Acad. Cienc. Exactas Fís....
  • J. E. Sampaio, Multiplicity, regularity and Lipschitz Geometry of real analytichypersurfaces, Israel J. Math. (to appear).
  • D. Trotman, Multiplicity is a C1 invariant, University Paris 11 (Orsay), Preprint (1977).
  • D. Trotman, Multiplicity as a C1 invariant, in: “Real Analytic and Algebraic Singularities” (Nagoya/Sapporo/Hachioji, 1996), Pitman Research...
  • G. Valette, Multiplicity mod 2 as a metric invariant, Discrete Comput. Geom.43(3) (2010), 663–679. DOI: 10.1007/s00454-009-9205-z.
  • H. Whitney, “Complex Analytic Varieties”, Addison-Wesley publishing company, Mass.-Menlo Park, Calif.-London-Don Mills, Ont, 1972.
  • O. Zariski, Some open questions in the theory of singularities, Bull. Amer. Math. Soc. 77(4) (1971), 481–491. DOI: 10.1090/s0002-9904-1971-12729-5.