On the Hilbert-Samuel partition of stable map-germs
Bulletin de la Société Mathématique de France, Tome 111 (1983), pp. 327-358. 
@article{BSMF_1983__111__327_0,
     author = {Damon, James and Galligo, Andr\'e},
     title = {On the {Hilbert-Samuel} partition of stable map-germs},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {327--358},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {111},
     year = {1983},
     doi = {10.24033/bsmf.1992},
     mrnumber = {86b:58012},
     zbl = {0547.58001},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/bsmf.1992/}
}
TY  - JOUR
AU  - Damon, James
AU  - Galligo, André
TI  - On the Hilbert-Samuel partition of stable map-germs
JO  - Bulletin de la Société Mathématique de France
PY  - 1983
SP  - 327
EP  - 358
VL  - 111
PB  - Société mathématique de France
UR  - http://archive.numdam.org/articles/10.24033/bsmf.1992/
DO  - 10.24033/bsmf.1992
LA  - en
ID  - BSMF_1983__111__327_0
ER  - 
%0 Journal Article
%A Damon, James
%A Galligo, André
%T On the Hilbert-Samuel partition of stable map-germs
%J Bulletin de la Société Mathématique de France
%D 1983
%P 327-358
%V 111
%I Société mathématique de France
%U http://archive.numdam.org/articles/10.24033/bsmf.1992/
%R 10.24033/bsmf.1992
%G en
%F BSMF_1983__111__327_0
Damon, James; Galligo, André. On the Hilbert-Samuel partition of stable map-germs. Bulletin de la Société Mathématique de France, Tome 111 (1983), pp. 327-358. doi : 10.24033/bsmf.1992. http://archive.numdam.org/articles/10.24033/bsmf.1992/

[1] Briançon (J.), Description de HilbnC {x,y}, Invent. Math., Vol. 41, 1977, pp. 45-89. | MR | Zbl

[2] Briançon (J.) et Galligo (A.), Déformations distinguées d'un point ℂ2 ou ℝ2, Singularités à Cargèse, Astérisque, Nos. 7 & 8, 1973, pp. 129-138. | Numdam | MR | Zbl

[3] Bruce (J. W.) and Giblin (P. J.), A stratification of the space of plane quartic curves, Proceedings London Math. Soc., Vol. 42, 1981, pp. 270-298. | MR | Zbl

[4] Damon (J.), Thom Polynomials for Contact Class Singularities, Thesis, Harvard Univ., 1972.

[5] Damon (J.), Investigating the Topological Stratification of Jet Spaces, Proc. 11th Colloq. Braz. Math. Soc., 1977, pp. 633-649. | MR

[6] Damon (J.), Topological Properties of Discrete Algebra Type I : The Hilbert-Samuel Function, Adv. in Math., Supp. Ser., Vol. 5, 1979, pp. 83-118 ; II: Real and Complex Algebras, Amer. J. Math., Vol. 101, No. 6, 1979, pp. 1219-1248. | MR | Zbl

[7] Damon (J.) and Galligo (A.), A Topological Invariant for Stable Map Germs, Invent. Math., Vol. 32, 1976, pp. 103-132. | MR | Zbl

[8] Galligo (A.), A propos du théorème de préparation de Weierstrass, Springer Lecture Notes in Math., n° 409, 1974, pp. 543-579. | MR | Zbl

[9] Gaffney (T.), A Lower Bound for the Dimension of the Smoothable Components in Hilb (d) (in preparation).

[10] Giblin (P. S.) and Gibson (C. G.), Regularity Conditions over the Exceptional Uni-Modular Families, Quart. J. Math. Oxford, ser. 32, 1981, pp. 23-43. | MR | Zbl

[11] Granger (M.), Géométrie des schémas de Hilbert ponctuels, Mémoires de la Soc. Math. France, n° 8, 1983, 84 p. | Numdam | MR | Zbl

[12] Haefliger (A.), Les singularités des applications différentiables, Seminar H. Cartan, exposé n° 7, 1. | Numdam | Zbl

[13] Hironaka (H.), Subanalytic Sets, Number Theory, Algebraic Geometry and Commutative Algebra, in honor of Y. Akizuki, Kinokuniya, Tokyo, 1973, pp. 453-493. | MR | Zbl

[14] Hironaka (H.), Triangulation of Algebraic Sets, Proc. Sym. Pure Math., Vol. 29, 1975, pp. 165-185. | MR | Zbl

[15] Iarrobino (A.), Reducibility of the Families of O-Dimensional Schemes on a Variety, Invent. Math., Vol. 15, 1972, pp. 72-77. | MR | Zbl

[16] Iarrobino (A.), Ponctual Hilbert Schemes, Memoirs of Amer. Math. Soc., No. 188, 1977. | Zbl

[17] Looijenga (E.), Semi-Universal Deformation of a Simple Elliptic Singularity : Part I Unimodularity, Topology, Vol. 16, 1977, pp. 257-262. | MR | Zbl

[18] Martinet (J.), Déploiements versels des applications différentiables et classification des applications stables, Singularités d'Applications différentiables, Plans-sur-Bex, Springer Lecture Notes in Math., Vol. 535, 1975, pp. 1-44. | MR | Zbl

[19] Mather (J.), Stability of C∞-mappings ; III Finitely Determined Map Germs, Publ. Math. I.H.E.S., Vol. 35, 1968, pp. 127-156 ; IV Classification of Stable Germs by R-Algebras, Publ. Math. I.H.E.S., Vol. 37, 1969, pp. 223-248 ; V Transversality, Adv. in Math., Vol. 4, 1970, pp. 301-336 ; VI The Nice Dimensions, Liverpool Singularities Symposium I, Springer Lecture Notes, Vol. 192, 1970, pp. 207-253.

[20] Mather (J.), Stratifications and Mappings, Dynamical Systems, M. PEIXOTO, Ed. Academic Press, 1973, pp. 195-232. | MR | Zbl

[21] Mather (J.), How to Stratify Mappings and Jet Spaces, Singularités d'Applications différentiables, Plans-sur-Bex, Springer Lecture Notes, Vol. 535, 1975, pp. 128-176. | MR | Zbl

[22] Spanier (E. H.), Algebraic Topology, 1966, McGraw-Hill, New York. | MR | Zbl

Cité par Sources :