Stability conditions and Stokes factors

Abstract

Let A be the category of modules over a complex, finite-dimensional algebra. We show that the space of stability conditions on A parametrises an isomonodromic family of irregular connections on P^1 with values in the Hall algebra of A. The residues of these connections are given by the holomorphic generating function for counting invariants in A constructed by D. Joyce.

Very minor changes. Final version. To appear in Inventiones

References in corpus (3)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Symplectic Manifolds and Isomonodromic Deformations
• Spaces of stability conditions

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