The largeness conjecture for gluings of complex analytic space germs

Let $(X,x)$, $(Y,y)$, and $(Z,z)$ be germs of complex analytic spaces, and let $(X,x)\sqcup_{(Z,z)}(Y,y)$ denote their gluing along $(Z,z)$. A gluing is large when the associated map $f$ is large.

Largeness conjecture. Every gluing

$$(X,x)\sqcup_{(Z,z)}(Y,y)$$

of complex analytic space germs is large.

The paper introduces weakly large, large, and strongly large gluings and gives examples of large gluings under additional hypotheses, but the assertion for every gluing remains open.