There's a very interesting text by Cumrun Vafa called [Geometric Physics](http://arxiv.org/pdf/hep-th/9810149v1).

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?