Lê constant families of singular hypersurfaces
DOI:
https://doi.org/10.4067/S0716-09172012000400002Keywords:
Lê constant families, polar varieties, familias constantes de Lê, variedades polares.Abstract
We investigate the constancy of the Le numbers of one parameter deformations F :(C X Cn, 0) — (C, 0) of holomorphic germs of functions f :(Cn, 0) — (C, 0) which have singular set with any dimension s > 1. WecharacterizeLe constant deformations in terms of the non-splitting of the polar varieties and also from the integral closure of the ideal Jz (F) in On+1 generated by the partial derivatives of F with respect to the variables z = (z!,...,zn)Downloads
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References
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[2] T. Gaffney & R. Gassler, Segre numbers J. Alg. Geometry, 8, pp. 695—736, (1999).
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[7] D. T. Lê and B. Teissier, Varietes polaires locales et classes de Chern de varietes singuleres. Annals of Math., 114, pp. 457—491, (1981).
[8] J. Lipman, Equimultiplicity, reduction, and blowing up. Commutative algebra (Fairfax, Va., 1979), pp. 111—147, Lecture Notes in Pure and Appl. Math., 68, Dekker, New York, (1982).
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[10] B. Teissier, Cycles evanescents, sections planes et conditions de Whitney, In Singularites a Cargese, Asterisque, nos. 07 et 08, Soc. Math. France, pp. 285—362, (1973).
[2] T. Gaffney & R. Gassler, Segre numbers J. Alg. Geometry, 8, pp. 695—736, (1999).
[3] T. Gaffney & D. Massey, Trends in equisingularity theory, Singularity theory (Liverpool, 1996), 207—248, London Math. Soc. Lecture Note Ser., 263, Cambridge Univ. Press, Cambridge, (1999).
[4] G. M. Greuel, Constant Milnor number implies constant multiplicity for quasihomogeneous singularities, Manuscripta Math. 56, pp. 159—166, (1986).
[5] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann. of Math. (2) 79, pp. 150—326, (1964).
[6] P. Ramanujam and D. T. Lê, The invariance of Milnor number implies the invariance of the topological type, Amer. Jour. Math. 98, pp. 67—78, (1976).
[7] D. T. Lê and B. Teissier, Varietes polaires locales et classes de Chern de varietes singuleres. Annals of Math., 114, pp. 457—491, (1981).
[8] J. Lipman, Equimultiplicity, reduction, and blowing up. Commutative algebra (Fairfax, Va., 1979), pp. 111—147, Lecture Notes in Pure and Appl. Math., 68, Dekker, New York, (1982).
[9] D. Massey, Lê cycles and hypersurface singularities, Lecture Notes in Mathematics, 1615, Springer-Verlag 1995. Notes of 1974 seminar at Ecole Polytechnique, Univ. de Grenoble (1976).
[10] B. Teissier, Cycles evanescents, sections planes et conditions de Whitney, In Singularites a Cargese, Asterisque, nos. 07 et 08, Soc. Math. France, pp. 285—362, (1973).
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2013-02-19
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How to Cite
[1]
“Lê constant families of singular hypersurfaces”, Proyecciones (Antofagasta, On line), vol. 31, no. 4, pp. 333–343, Feb. 2013, doi: 10.4067/S0716-09172012000400002.
