Non-Kähler C-Y 3-folds arising from singular K3 surfaces

Abstract

In the paper, we study the blow-ups at singular points of a singular K3 surface and analyze the change in the Picard group during this process. Our aim is to produce examples of such surfaces that serve as the base of Seifert fibrations, carrying a non-Kähler complex structure with a trivial canonical bundle. These spaces can be explicitly identified up to a diffeomorphism and are natural candidates for solutions of the Hull-Strominger system.