Linearity of stability conditions

Abstract

For modules over an artin algebra a linear stability condition is given by a "central charge" and a nonlinear stability condition is given by the wall-crossing sequence of a "green path". Finite Harder-Narasimhan stratifications of the module category, maximal forward hom-orthogonal sequences and maximal green sequences, defined using Fomin-Zelevinsky quiver mutation are shown to be equivalent to finite nonlinear stability conditions when the algebra is hereditary. This is the first of a series of three papers whose purpose is to determine all maximal green sequences of maximal length for quivers of affine type A and determine which are linear. See [1].

27 pages, 3 figures, final version

References in corpus (6)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Modulated semi-invariants
• Stability conditions, $\tau$-tilting Theory and Maximal Green Sequences
• A survey on maximal green sequences
• Remarks on lengths of maximal green sequences for quivers of type ${\tilde{A}}_{n,1}$
• On maximal green sequences in abelian length categories

Cited by in corpus (6)

• Wall and Chamber Structure for finite-dimensional Algebras
• A survey on maximal green sequences
• An algebraic approach to Harder-Narasimhan filtrations
• On maximal green sequences in abelian length categories
• Maximal green sequences of quivers with multiple edges
• Horizontal and vertical mutation fans