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

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

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

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     author = {Buium, Alexandru},
     title = {Killing divisor classes by algebraisation},
     journal = {Annales de l'Institut Fourier},
     pages = {107--115},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {35},
     number = {2},
     year = {1985},
     doi = {10.5802/aif.1012},
     zbl = {0546.14031},
     mrnumber = {86m:32017},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1012/}
}
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Buium, Alexandru. Killing divisor classes by algebraisation. Annales de l'Institut Fourier, Tome 35 (1985) no. 2, pp. 107-115. doi : 10.5802/aif.1012. https://aif.centre-mersenne.org/articles/10.5802/aif.1012/

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

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

[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 | Zbl

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

[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 | Zbl

[7] J. Kollàr, letter 1983.

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

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

[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

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