On the image of an algebraic projective space

Blow‐ups and modifications of lcK spaces

“…Next, we define quasi‐Kähler and quasi‐lcK metrics by allowing $$-\infty$$ as a value for the system of strictly plurisubharmonic functions. The definition for quasi‐Kähler metrics was introduced in [2], but we also require $$\mathcal {C}^\infty$$‐regularity, as in [8]. Definition Let $$X$$ be a complex space.…”

“…It turns out that this is achieved simply by working with a more general definition than that of lcK metrics and allowing the strictly plurisubharmonic functions that locally define the metric to take the value $$-\infty$$ on a controlled set of points. We call this type of metric a quasi‐lcK metric , inspired by the notion of quasi‐Kähler metric introduced by Colţoiu [2], and later used by Popa–Fischer [8] under the name of generalized Kähler metric . The result we prove here is the following.…”