A class of non-algebraic threefolds

The paper is published: Ann. Inst. Fourier Grenoble, 39 (1989), 239-250

MSC 2000

32J15 Compact surfaces

32J17 Compact $3$-folds

32L05 Holomorphic bundles and generalizations

Abstract
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.

Keywords: holomorphic vector bundle, compact complex surface, nonalgebraic surface, complex threefold