Multiplicity estimates and the product theorem
Bulletin de la Société Mathématique de France, Tome 123 (1995) no. 2, pp. 155-188. 
@article{BSMF_1995__123_2_155_0,
     author = {Nakamaye, Michael},
     title = {Multiplicity estimates and the product theorem},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {155--188},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {123},
     number = {2},
     year = {1995},
     doi = {10.24033/bsmf.2255},
     mrnumber = {96i:14038},
     zbl = {0841.11037},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/bsmf.2255/}
}
TY  - JOUR
AU  - Nakamaye, Michael
TI  - Multiplicity estimates and the product theorem
JO  - Bulletin de la Société Mathématique de France
PY  - 1995
SP  - 155
EP  - 188
VL  - 123
IS  - 2
PB  - Société mathématique de France
UR  - http://archive.numdam.org/articles/10.24033/bsmf.2255/
DO  - 10.24033/bsmf.2255
LA  - en
ID  - BSMF_1995__123_2_155_0
ER  - 
%0 Journal Article
%A Nakamaye, Michael
%T Multiplicity estimates and the product theorem
%J Bulletin de la Société Mathématique de France
%D 1995
%P 155-188
%V 123
%N 2
%I Société mathématique de France
%U http://archive.numdam.org/articles/10.24033/bsmf.2255/
%R 10.24033/bsmf.2255
%G en
%F BSMF_1995__123_2_155_0
Nakamaye, Michael. Multiplicity estimates and the product theorem. Bulletin de la Société Mathématique de France, Tome 123 (1995) no. 2, pp. 155-188. doi : 10.24033/bsmf.2255. http://archive.numdam.org/articles/10.24033/bsmf.2255/

[B] Bertrand (D.). - Lemmes de zéros et nombres transcendants, Séminaire Bourbaki, 38-ème année, 1985-86, exposé n° 652, S.M.F. Astérisque, 145-146, 1987, p. 21-44. | Numdam | MR | Zbl

[BEL] Bertram (A.), Ein (L.) and Lazarsfeld (R.). - Vanishing theorems, a theorem of Severi, and the equations defining projective varieties, Journal of the AMS, t. 4, 3, 1991, p. 587-602. | MR | Zbl

[Br] Brownawell (W.D.). - Note on a paper of P. Philippon, Michigan Math J., t. 34, 1987, p. 461-464. | MR | Zbl

[CH] Chow (W.L.). - On the projective embedding of homogeneous varieties, in Algebraic Geometry and Topology: A Symposium in Honor of S. Lefschetz, Princeton University Press, 1957, p. 122-28.. | MR | Zbl

[EL] Ein (L.) and Lazarsfeld (R.). - Syzygies and Koszul cohomology of smooth projective varieties of arbitrary dimension, Invent. Math., t. 111, 1993, p. 51-67. | MR | Zbl

[F] Faltings (G.). - Diophantine Approximation on Abelian Varieties, Ann. of Math., t. 133, 1991, p. 549-576. | MR | Zbl

[F-L] Fulton (W.) and Lazarsfeld (R.). - Positivity and excess intersections, in Enumerative and classical geometry, Nice 1981, Progress in Math. 24, Birkhäuser, 1982, p. 97-105. | MR | Zbl

[Fu] Fulton (W.). - Intersection Theory. - Springer Ergebnisse, 1984. | MR | Zbl

[G] Van Gastel (L.J.). - Excess intersections and a correspondence principle, Invent. Math., t. 103, 1991, p. 197-221. | MR | Zbl

[G-G] Golubitsky (M.) and Guillemin (V.). - Stable Mappings and Their Singularities. - Springer, 1973. | MR | Zbl

[G-R] Grauert (H.) and Remmert (R.). - Coherent Analytic Sheaves. - Springer Grundlehren 265, 1984. | MR | Zbl

[H] Hartshorne (R.). - Algebraic Geometry. - Springer-Verlag, 1977. | MR | Zbl

[K] Kleiman (S.L.). - The transversality of a general translate, Compositio Math., t. 38, 1974, p. 287-297. | Numdam | MR | Zbl

[KL1] Knop (F.) and Lange (H.). - Commutative algebraic groups and intersections of quadrics, Math. Ann., t. 267, 1984, p. 555-71. | MR | Zbl

[KL2] Knop (F.) and Lange (H.). - Some remarks on compactifications of commutative algebraic groups, Comment. Math. Helv., t. 60, 1985, p. 497-507. | MR | Zbl

[L] Lange (H.). - Families of translations of commutative algebraic groups, J. Algebra, t. 109, 1987, p. 260-65. | MR | Zbl

[La1] Lang (S.). - Hyperbolic and Diophantine Analysis, Bull. Amer. Math. Soc., t. 14, 1986, p. 159-205. | MR | Zbl

[La2] Lang (S.). - Fundamentals of Diophantine Geometry. - Springer, 1983. | MR | Zbl

[Ma] Matsumura (H.). - Commutative Ring Theory. - Cambridge University Press, 1986. | MR | Zbl

[M] Masser (D.W.). - Zero estimates on group varieties, Proc. ICM, Warszawa, 1983, vol. 1, p. 493-502. | MR | Zbl

[MW1] Masser (D.W.) and Wüstholz (G.). - Zero estimates on group varieties I, Invent. Math., t. 64, 1981, p. 489-516. | MR | Zbl

[MW2] Masser (D.W.) and Wüstholz (G.). - Zero estimates on group varieties II, Invent. Math., t. 80, 1985, p. 233-267. | MR | Zbl

[Mo] Moreau (J.-C.). - Démonstrations géométriques de lemmes de zéros II, Birkhäuser Prog. Math., t. 31, 1983, p. 191-7. | MR | Zbl

[N] Nesterenko (Y.). - Estimates for orders of zeroes of functions of a certain class and applications in the theory of transcendental numbers, Math USSR Izv., t. 11, 1977, p. 239-270. | Zbl

[P-V] Patil (D.P.) and Vogel (W.). - Remarks on the algebraic approach to intersection theory, Monatsh. Math., t. 96, 1983, p. 233-250. | MR | Zbl

[P1] Philippon (P.). - Lemmes de zéros dans les groupes algébriques commutatifs, Bull. Soc. Math. France, t. 114, 1986, p. 355-383. | Numdam | MR | Zbl

[P2] Philippon (P.). - Errata et addenda à "Lemmes de zéros dans les groupes algébriques commutatifs", Bull. Soc. Math. France, t. 115, 1987, p. 397-398. | Numdam | MR | Zbl

[S-V] Stückrad (J.) and Vogel (W.). - An algebraic approach to intersection theory, in Geramita, A. V. (ed.) The Curves Seminar at Queen's University, Vol. II, Queen's papers Pure Appl. Math. 61 (1982), p. 1-32. | MR | Zbl

[V] Vogel (W.). - Results on Béezout's theorem, Tata Lecture Notes vol. 74, Springer, 1984. | MR | Zbl

[W1] Wüstholz (G.). - Neue Methoden in der Theorie der transzendenten Zahlen. - Habilitationsschrift, Wuppertal, 1982.

[W2] Wüstholz (G.). - Multiplicity estimates on group varieties, Ann. of Math., t. 129, 1989, p. 471-500. | MR | Zbl

[Wa] Van Der Waerden (B.L.). - On Hilbert's function, series of composition of ideals and a generalization of the theorem of Bézout, Proc. Roy. Soc. Amsterdam, t. 31, 1929, p. 749-770. | JFM

[Wa1] Waldschmidt (M.). - Nombres transcendants et groupes algébriques, Astérisque, t. 69-70, 1979. | Numdam | MR | Zbl

Cité par Sources :