Publication: Lê’s conjecture for cyclic covers
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Publication Date
2005
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Société Mathématique de France
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Abstract
We describe the link of the cyclic cover over a singularity of complex surface (S, p) totally branched over the zero locus of a germ of analytic function (S, p) ! (C, 0).As an application, we prove Lê’s conjecture for this family of singu-larities i.e. that if the link is homeomorphic to the 3-sphere then the singularity is an equisingular family of unibranch curves.
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Singularités franco-japonaises
Jean-Paul Brasselet - Tatsuo Suwa (Éd.)
Séminaires et Congrès 10 (2005), xxxii+460 pages
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N. Chavez – Variétés graphées fibrées sur le cercle et difféomorphismes quasi-finis de surfaces, Ph.D. Thesis, University of Geneva, Switzerland, 1996.
P. Du Bois & F. Michel – The integral Seifert form does not determine the topology of plane curve germs, J. Algebraic Geom. 3 (1994), p. 1–38.
A. Durfee – Neighbourhoods of algebraic sets, Trans. Amer. Math. Soc. 276 (1983), p. 517–530.
D. Eisenbud & W. Neumann – Three-dimensional link theory and invari ants of plane curve singularities, Annals of Mathematics Studies, vol. 110, Princeton University Press, Princeton, NJ, 1985.
H. Grauert – Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962), p. 331–368.
W. Jaco & P. Shalen – Seifert fibred spaces in three-manifolds, Mem. Amer. Math. Soc., vol. 220, American Mathematical Society, Providence, RI, 1979.
Lê D.T., H. Maugendre & C. Weber – Geometry of critical loci, J. London Math. Soc. (2) 63 (2001), no. 3, p. 533–552.
Lê D.T., F. Michel & C. Weber – Courbes polaires et topologie des courbes planes, Ann. scient. Éc. Norm. Sup. 4e série 24 (1991), p. 141–169.
Lê D.T. & C. Weber – Équisingularité dans les pinceaux de germes de courbes planes et C0-suffisance, Enseign. Math. 43 (1997), p. 355–380.
I. Luengo – The μ-constant stratum is not smooth, Invent. Math. 90 (1987), no. 1, p. 139–152.
I. Luengo, A. Melle-Hernández & A. Pichon – on the singularities with equations fd + fd+k=0, in preparation.
L. McEwan & A. Nemethi – Some conjectures about quasi-ordinary singularities, preprint.
J. Milnor – Singular points of complex hypersurfaces, Annals of Mathematics Studies, vol. 61, Princeton University Press, Princeton, NJ, 1968.
A. Némethi & A. Szilárd – The resolution of some surface singularities, II (Iomdin’s series), in Singularities in Algebraic and Analytic Geometry, Proceedings of the AMS
Conference, San Antonio, 1999 (C.G. Melles & R.I.Michler, eds.), ContemporaryMathematics, vol. 266, American Mathematical Society, Providence, RI, 2000, p. 129–164.
W.D. Neumann – A calculus for plumbing applied to the topology of complex surface singularities and degenerating complex curves,Trans. Amer. Math. Soc. 268(1981),p. 299–344.
A. Pichon – Three-dimensional manifolds which are the boundary of a normal singularity zk− f(x, y) = 0, Math. Z. 231 (1999), p. 625–654.
Fibrations sur le cercle et surfaces complexes, Ann. Inst. Fourier (Grenoble) 51 (2001), p. 337–374.
F. Waldhausen – Eine klasse von 3-dimensionalen Mannifaltigkeiten II, Invent. Math.4 (1967), p. 87–117.
C.Weber (ed.) – Noeuds, tresses et singularités. Proceedings of the seminar held in Plans-sur-Bex, March 27-April 2 1982, Monographies de L’Enseignement Mathématique, vol. 31, 1983.