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arXiv · 1706.06986

Linearity of stability conditions

Kiyoshi Igusa
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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].

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Kiyoshi Igusa. 2017-06-21. Linearity of stability conditions. https://doi.org/10.1080/00927872.2019.1705466

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