Quivers

quiverDefinition 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;

 

2-cycle loop

 

 

 

 

 

 

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.

 

 

 

 

 

 

 

 

picture 4

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

 

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