Number of singular points of an annulus in $\mathbb{C}^2$

Borodzik, Maciej; Zołądek, Henryk

doi:10.5802/aif.2650

Number of singular points of an annulus in

ℂ^{2}

[Le nombre de points singuliers d’un anneau dans

ℂ^{2}

]

Borodzik, Maciej ¹ ; Zołądek, Henryk ²

¹ University of Warsaw Institute of Mathematics ul. Banacha 2 02-097 Warsaw (Poland)
² Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland

Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1539-1555.

Résumé
Abstract

Utilisant l’ inégalité BMY et une évaluation pour le nombre de Milnor nous prouvons que chaque anneau $ℂ^{*}$ dans $ℂ^{2}$ sans auto-intersections ne peut avoir qu’ au plus trois singularités cuspidalles

Using BMY inequality and a Milnor number bound we prove that any algebraic annulus $ℂ^{*}$ in $ℂ^{2}$ with no self-intersections can have at most three cuspidal singularities.

MR Zbl

DOI : 10.5802/aif.2650

Classification : 14H50, 14R10, 14B05
Keywords: Annulus, cuspidal singular point, codimension
Mot clés : annulus, point singulier cuspidal, codimension

Affiliations des auteurs :

Borodzik, Maciej ¹ ; Zołądek, Henryk ²

¹ University of Warsaw Institute of Mathematics ul. Banacha 2 02-097 Warsaw (Poland)
² Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland

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     author = {Borodzik, Maciej and Zo{\l}\k{a}dek, Henryk},
     title = {Number of singular points of an annulus in $\mathbb{C}^2$},
     journal = {Annales de l'Institut Fourier},
     pages = {1539--1555},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {61},
     number = {4},
     year = {2011},
     doi = {10.5802/aif.2650},
     zbl = {1238.14049},
     mrnumber = {2951503},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.2650/}
}

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Borodzik, Maciej; Zołądek, Henryk. Number of singular points of an annulus in $\mathbb{C}^2$. Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1539-1555. doi : 10.5802/aif.2650. http://www.numdam.org/articles/10.5802/aif.2650/

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