Quivers
Definition and examples
As is well known in archery, a quiver is a container where arrows are kept. An example is the diagram on the left. An immediate queston is how this concept is linked to mathematics.
Just like oriental quivers, which have a source and a target, so does mathematical quivers. In mathematics, a quiver is an oriented graph. It consists of a sset of arrows, a set of points (vertices), and two maps assigning to each arrow the starting and terminating points. With this definition, multiple arrows are allowed between vertices. Examples of quivers are;
Quiver diagrams can be simple with only a few arrows and points, it can also be very complicated when the sets of points and arrows get too large, or when arrows join the points in complicated patterns.
The number in the arrows indicate the number of arrows while we have given the points names, for identification.
It is an example of a quiver with multiple arrows between points.
Mutation of quivers
These are example of a del-Pezzo quivers. Losely speaking, the number in the point can be considered as the size of the point. Each point in a del-Pezzo quiver has a size.
More examples of del-Pezzo quivers
Quivers with r-charge