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makeTight -- return a tight quiver with the same flow polytope

Description

Let $\theta$ be an integral weight assigned to the vertices of a quiver $Q$. The quiver $Q$ is called $\theta$-tight if for every arrow $\alpha$, the subquiver $Q\setminus \alpha$ is $\theta$-stable. Every quiver can be tightened by contraction of certain arrows in Q and changing the weight accordingly, see Section 4 at Altmann, Klaus, and Duco van Straten. "Smoothing of quiver varieties." manuscripta mathematica 129 (2009): 211-230.

i1 : Q = bipartiteQuiver(2, 3);
i2 : w = {-5,-1,2,2,2};
i3 : makeTight(w, Q)

o3 = ToricQuiver{flow => {0, -1, 1, 1}                 }
                 IncidenceMatrix => | -1 1  1  0  |
                                    | 0  -1 -1 -1 |
                                    | 1  0  0  1  |
                 Q0 => {0, 1, 2}
                 Q1 => {{0, 2}, {1, 0}, {1, 0}, {1, 2}}
                 weights => {0, -1, 1}

o3 : ToricQuiver

For the programmer

The object makeTight is a function closure.


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/ThinSincereQuivers.m2:3279:0.