Geodesic
Algebraic homology classes on algebraic varieties
Izvestiya. Mathematics, Tome 1 (1967) no. 2, pp. 209-251 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, the relation between the algebraic homology classes on a protective algebraic variety and on its “general” hyperplane section is studied. It is proved in particular that on a “general” section of an algebraic variety $V$ by a hypersurface of sufficiently high degree, any algebraic homology class, taken with some multiplicity, is cut by some algebraic homology class of the variety $V$. 
@article{IM2_1967_1_2_a1,
     author = {B. G. Moishezon},
     title = {Algebraic homology classes on algebraic varieties},
     journal = {Izvestiya. Mathematics},
     pages = {209--251},
     year = {1967},
     volume = {1},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a1/}
}
TY  - JOUR
AU  - B. G. Moishezon
TI  - Algebraic homology classes on algebraic varieties
JO  - Izvestiya. Mathematics
PY  - 1967
SP  - 209
EP  - 251
VL  - 1
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a1/
LA  - en
ID  - IM2_1967_1_2_a1
ER  - 
%0 Journal Article
%A B. G. Moishezon
%T Algebraic homology classes on algebraic varieties
%J Izvestiya. Mathematics
%D 1967
%P 209-251
%V 1
%N 2
%U http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a1/
%G en
%F IM2_1967_1_2_a1
B. G. Moishezon. Algebraic homology classes on algebraic varieties. Izvestiya. Mathematics, Tome 1 (1967) no. 2, pp. 209-251. http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a1/

[1] Lefschetz S., L'analysis situs et la géometrie algébrique, Paris, 1924

[2] Lefschetz S., “On certain numerical invariants of algebraic varieties with applications to Abelian varieties”, Trans. Amer. Math. Soc., 22 (1921), 327–482 | DOI | MR | Zbl

[3] Andreotti A., Salmon P., “Anelli con unica decomponibilità in fattori primi ed un problema di intersezioni complete”, Monatsh. Math., 61:2 (1957), 97–142 | DOI | MR | Zbl

[4] Fary J., “Gohomologie des variétés algebriques”, Ann. Math., 65 (1957), 21–73 | DOI | MR | Zbl

[5] Zhizhchenko A. B., “O gruppakh gomologii algebraicheskikh mnogoobrazii”, Izv. AN SSSR. Ser. matem., 25 (1961), 765–788 | Zbl

[6] Stinrod N., Topologiya kosykh proizvedenii, M., 1953

[7] Kodaira K., “O kompaktnykh analiticheskikh poverkhnostyakh. I”, Matematika, 6:6 (1962), 20–57

[8] Khodzh V., Pido D., Metody algebraicheskoi geometrii, t. II, M., 1954

[9] Kodaira K., “O differentsialno-geometricheskom metode v teorii analiticheskikh puchkov”, Matematika, 2:6 (1958), 126–131 | MR

[10] Chzhen-Shen-Shen, Kompleksnye mnogoobraziya, M., 1961

[11] Baldassarri M., Algebraicheskie mnogoobraziya, M., 1961 | MR

[12] Gherardelli F., “Un teorema di Lefschetz sulle intersezioni complete”, Atti Accad. naz. Lincei. Red. CI. sci. fis., mat. e natur., 28:5 (1960), 610–614 | MR | Zbl

[13] Andreotti A., Frankel T., “The Lefschetz theorem on hyperplane sections”, Ann. Math., 69 (1959), 713–717 | DOI | MR | Zbl

[14] Serr Zh.-P., “Kogerentnye algebraicheskie puchki”, Rassloennye prostranstva, M., 1958