Stability conditions and the $A_2$ quiver

Abstract

For each integer $n\ge 2$ we describe the space of stability conditions on the derived category of the $n$-dimensional Ginzburg algebra associated to the $A_2$ quiver. The form of our results points to a close relationship between these spaces and the Frobenius-Saito structure on the unfolding space of the $A_2$ singularity.

Isotopy to the published version

References in corpus (6)

• Calabi-Yau algebras
• Flat surfaces and stability structures
• q-Stability conditions on Calabi-Yau-X categories
• $q$-Stability conditions via $q$-quadratic differentials for Calabi-Yau-$\mathbb{X}$ categories
• Stability conditions on ${\text{CY}}_N$ categories associated to $A_n$-quivers and period maps
• Stability conditions and braid group actions on affine $A_n$ quivers

Cited by in corpus (15)

• Flat surfaces and stability structures
• Categorical polynomial entropy
• On the monodromy of the deformed cubic oscillator
• q-Stability conditions on Calabi-Yau-X categories
• On pseudo-Anosov autoequivalences
• $q$-Stability conditions via $q$-quadratic differentials for Calabi-Yau-$\mathbb{X}$ categories
• Global dimension function on stability conditions and Gepner equations
• A Thurston compactification of the space of stability conditions
• Stability conditions on ${\text{CY}}_N$ categories associated to $A_n$-quivers and period maps
• Asymptotic shifting numbers in triangulated categories
• T-stabilities for a weighted projective line
• Topological structure of spaces of stability conditions and topological Fukaya type categories
• Discrete derived categories II: The silting pairs CW complex and the stability manifold
• A construction of Frobenius manifolds from stability conditions
• A local compactification of the Bridgeland stability manifold