There's a very interesting text by Cumrun Vafa called Geometric Physics.

Here I'm particularly interested in Chapter 4, where we take a Calabi-Yau manifold presented as a degenerating fibration:

The appearance of the Dynkin structure for the K3 singularities appears mathematically as purely “accidental”. However this accident gets explained in this duality context: One identifies the singular K3 geometries with A-D-E singularities with the points on the heterotic side with enhanced A-D-E gauge symmetry...

I look at the pictures (p.15) and I have a very simple question:

• Is this vanishing K3 obtainable as a vanishing/nearby cycle functor for the cohomology of the fibration?

If it is, I will finally have an example of the abovementioned functor. If not, how to describe this K3 from a math point of view? One possible way would be to vary Kahler parameters and get a true, finite-size K3. Other descriptions?