On locally conformally Kähler threefolds with algebraic dimension two

19 May 2020 · Daniele Angella, Maurizio Parton, Victor Vuletescu ·

The paper is part of an attempt of understanding non-K\"ahler threefolds. We start by looking at compact complex non-K\"ahler threefolds with algebraic dimension two and admitting locally conformally K\"ahler metrics. Under certain assumptions, we prove that they are blown-up quasi-bundles over a projective surface.