A class of non-algebraic threefolds
Annales de l'Institut Fourier, Volume 39 (1989) no. 1, p. 239-250

Let X be a compact complex nonsingular surface without curves, and E a holomorphic vector bundle of rank 2 on X. It turns out that the associated projective bundle PE has no divisors if and only if E is “strongly” irreducible. Using the results concerning irreducible bundles of [Banica-Le Potier, J. Crelle, 378 (1987), 1-31] and [Elencwajg- Forster, Annales Inst. Fourier, 32-4 (1982), 25-51] we give a proof of existence for bundles which are strongly irreducible.

Soit X une surface C-analytique, compacte, lisse, sans diviseurs, et E un fibré vectoriel holomorphe de rang 2 sur X. Le fibré projectif associé, P(E), n’aura pas de diviseurs si et seulement si E est “fortement” irréductible. On prouve l’existence de tels fibrés.

@article{AIF_1989__39_1_239_0,
     author = {Toma, Matei},
     title = {A class of non-algebraic threefolds},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {39},
     number = {1},
     year = {1989},
     pages = {239-250},
     doi = {10.5802/aif.1166},
     zbl = {0659.32024},
     mrnumber = {90k:32084},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1989__39_1_239_0}
}
Toma, Matei. A class of non-algebraic threefolds. Annales de l'Institut Fourier, Volume 39 (1989) no. 1, pp. 239-250. doi : 10.5802/aif.1166. http://www.numdam.org/item/AIF_1989__39_1_239_0/

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