Algebraic approximation of Kähler threefolds

Details Algebraic approximation of Kähler threefolds Algebraic approximation of Kähler threefolds

2011-12-07

arxiv.org/abs/1112.1518v1

Mathematics

Algebraic Geometry

19 pages; accepted for publication in Mathematische Nachrichten

Scientific paper

In the present work, we investigate existence of deformations and algebraic approximability for certain uniruled K\"ahler threefolds. In the first part, we establish existence of infinitesimal deformations for all conic bundles with relative Picard number one over a non-algebraic compact K\"ahler surface S and existence of positive-dimensional families of deformations in all but some special cases. In the second part, we study the question of algebraic approximability for projective bundles over S and threefolds bimeromorphic to P_1 x S.

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