E8 and the minimal resolution

What sits above the singularity in the minimal resolution?

8 copies of the Riemann sphere ℂP¹, one for each dot here:

Two of these ℂP¹'s intersect in a point if their dots are connected by an edge: otherwise they're disjoint!

For a quick introduction see Section 5.2 here:

For details, see Chapter IV here:

Klaus Lamotke, Regular Solids and Isolated Singularities, Vieweg & Sohn, Braunschweig, 1986.