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A class of non-algebraic threefolds

Matei Toma (1989)

Annales de l'institut Fourier

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 P E 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.

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