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quiverWeights -- return the weight attribute associated to the toric quiver

Synopsis

Description

This method returns the weights of the provided toric quiver. The weights are the image of the quiver flow under the inc map, which is defined as $$ \text{inc}(\mathbf{w})(i) := \sum_{a\in Q_1 \atop a^{+} = i} \mathbf{w}(a) - \sum_{a\in Q_1 \atop a^{-} = i} \mathbf{w}(a) \quad \text{ for all } i \in Q_0. $$ where for any arrow $a\in Q_1$, we denote its head as $a^{+} \in Q_0$ and its tail as $a^{-} \in Q_0$.

i1 : Q = bipartiteQuiver(2, 3);
i2 : quiverWeights Q

o2 = {-3, -3, 2, 2, 2}

o2 : List

See also

Ways to use quiverWeights :

For the programmer

The object quiverWeights is a method function.