Killing divisor classes by algebraisation
Annales de l'Institut Fourier, Volume 35 (1985) no. 2, p. 107-115

It is proved that any isolated singularity of complete intersection has an algebraisation whose divisor class group is finitely generated.

On démontre que toute singularité isolée d’intersection complète possède une algébrisation dont le groupe des classes de diviseurs est de type fini.

@article{AIF_1985__35_2_107_0,
     author = {Buium, Alexandru},
     title = {Killing divisor classes by algebraisation},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {35},
     number = {2},
     year = {1985},
     pages = {107-115},
     doi = {10.5802/aif.1012},
     zbl = {0546.14031},
     mrnumber = {86m:32017},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1985__35_2_107_0}
}
Buium, Alexandru. Killing divisor classes by algebraisation. Annales de l'Institut Fourier, Volume 35 (1985) no. 2, pp. 107-115. doi : 10.5802/aif.1012. http://www.numdam.org/item/AIF_1985__35_2_107_0/

[1] A. Buium, A note on the class group of surfaces in 3-space, to appear in Journal of Pure and Applied Algebra. | Zbl 0584.14026

[2] P. Deligne, Théorie de Hodge II, IHES Publ. Math., 40 (1971), 5-58. | Numdam | MR 58 #16653a | Zbl 0219.14007

[3] W. Fulton and R. Lazarsfeld, Connectivity and its applications in algebraic geometry, in Algebraic Geometry, Lecture Notes in Math. 862 (Spriger, Berlin-Heidelberg-New York, 1981). | MR 83i:14002 | Zbl 0484.14005

[4] H. Grauert and O. Riemenschneider, Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen, Invent. Math., 11 (1970), 263-292. | MR 46 #2081 | Zbl 0202.07602

[5] A. Grothendieck, Cohomologie des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux, SGA II (North-Holland, Paris-Amsterdam, 1969).

[6] R. Hartshorne, Algebraic Geometry (Springer, New York-Heidelberg Berlin, 1977). | MR 57 #3116 | Zbl 0367.14001

[7] J. Kollàr, letter 1983.

[8] K. Lamotke, The topology of complex projective varieties after S. Lefschetz, Topology, 20 (1981), 15-51. | MR 81m:14019 | Zbl 0445.14010

[9] J. N. Mather, Stability of C∞ mappings III, IHES Publ. Math., 35 (1969), 127-156. | Numdam | Zbl 0159.25001

[10] B. Moishezon, Algebraic cohomology classes on algebraic manifolds (in russian), Izvestia Akad. Nauk SSSR, 31 (1967), 225-268.

[11] N. Bourbaki, Algèbre commutative, Chapitre 7: Diviseurs (Hermann, Paris, 1965). | Zbl 0141.03501