We mutate these quivers at the blue point.
Mutation of quivers
Mutation of del-Pezzo quivers
The special thing with del-Pezzo quivers is that we associate sizes to points. We will mutate examples of these quivers which are from geometry.
As you will realize, the process is the same only that there is an added step which takes care of the size of points.
Step 1.
There is a new number at the blue point given by
(Total arrow in size)- (old size):
Other points of the quiver remain unchanged
Step 2.
Arrows into the blue point in the original quiver gives arrows out of the blue pointin the new quiver.
Step 3.
Arrows out of the blue poin tin the original quiver gives arrows into the blue pointin the new quiver.
Step 4.
Arrows not to or from the blue point in the original quiver remain unchanged in the new quiver.
Step 5.
Any path of length 2 through the blue point in the original quiver gives an arrow from the start to the end of the path in the new quiver
Step 6.
We simplify the mutated quiver by getting the difference between arrows joining any two points but in opposite direction.
As it turns out, even with the del-Pezzo quivers, we can get back to our original quiver by repeating the process of mutation at the very point, In our case the blue point. .