Bridgeland stability conditions on the acyclic triangular quiver
Let $k$ be an algebraically closed field, let $Q$ be the only affine acyclic quiver with three vertices, $\mathrm{Rep}_k(Q)$ -- the category of $k$-representations of $Q$ and $D^b(\mathrm{Rep}_k(Q)$ -- the derived category of $\mathrm{Rep}_k(Q)$. The authors prove that the space of Bridgeland stability conditions $\mathrm{Stab}(D^b(\mathrm{Rep}_k(Q)))$ is a contractible (in particular connected) manifold. This is the first example of quiver $Q$ (different from Dynkin and Kronecker quivers) with this property. To prove the main theorem the authors develop their previous results presented in ``Non-semistable exceptional objects in hereditary categories''. The motivation for this research is its connection with homological mirror symmetry.
Bridgeland stability conditions on triangulated categories
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