On the Hilbert-Samuel partition of stable map-germs
Damon, James ; Galligo, André
Bulletin de la Société Mathématique de France, Tome 111 (1983), p. 327-358 / Harvested from Numdam
@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},
     volume = {111},
     year = {1983},
     pages = {327-358},
     doi = {10.24033/bsmf.1992},
     mrnumber = {86b:58012},
     zbl = {0547.58001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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://gdmltest.u-ga.fr/item/BSMF_1983__111__327_0/

[1] Briançon (J.), Description de HilbnC {x,y}, Invent. Math., Vol. 41, 1977, pp. 45-89. | MR 56 #15637 | Zbl 0353.14004

[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. | MR 50 #13585 | Zbl 0291.14004

[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 82j:14022 | Zbl 0403.14004

[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 80k:58019

[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 80e:58009 | Zbl 0498.58005

[7] Damon (J.) and Galligo (A.), A Topological Invariant for Stable Map Germs, Invent. Math., Vol. 32, 1976, pp. 103-132. | MR 53 #11653 | Zbl 0333.57017

[8] Galligo (A.), A propos du théorème de préparation de Weierstrass, Springer Lecture Notes in Math., n° 409, 1974, pp. 543-579. | MR 53 #5924 | Zbl 0297.32003

[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 82g:58016 | Zbl 0472.58007

[11] Granger (M.), Géométrie des schémas de Hilbert ponctuels, Mémoires de la Soc. Math. France, n° 8, 1983, 84 p. | Numdam | MR 86d:14004 | Zbl 0534.14002

[12] Haefliger (A.), Les singularités des applications différentiables, Seminar H. Cartan, exposé n° 7, 1. | Numdam | Zbl 0178.26603

[13] Hironaka (H.), Subanalytic Sets, Number Theory, Algebraic Geometry and Commutative Algebra, in honor of Y. Akizuki, Kinokuniya, Tokyo, 1973, pp. 453-493. | MR 51 #13275 | Zbl 0297.32008

[14] Hironaka (H.), Triangulation of Algebraic Sets, Proc. Sym. Pure Math., Vol. 29, 1975, pp. 165-185. | MR 51 #10331 | Zbl 0332.14001

[15] Iarrobino (A.), Reducibility of the Families of O-Dimensional Schemes on a Variety, Invent. Math., Vol. 15, 1972, pp. 72-77. | MR 46 #170 | Zbl 0227.14006

[16] Iarrobino (A.), Ponctual Hilbert Schemes, Memoirs of Amer. Math. Soc., No. 188, 1977. | Zbl 0355.14001

[17] Looijenga (E.), Semi-Universal Deformation of a Simple Elliptic Singularity : Part I Unimodularity, Topology, Vol. 16, 1977, pp. 257-262. | MR 56 #8565 | Zbl 0373.32004

[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 58 #31178 | Zbl 0362.58004

[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 51 #4306 | Zbl 0286.58003

[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 56 #13259 | Zbl 0398.58008

[22] Spanier (E. H.), Algebraic Topology, 1966, McGraw-Hill, New York. | MR 35 #1007 | Zbl 0145.43303