Linearity of stability conditions |
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Authors: | Kiyoshi Igusa |
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Affiliation: | 1. Department of Mathematics, Brandeis University, Waltham, Massachusetts, USAigusa@brandeis.edu |
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Abstract: | AbstractFor 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. |
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Keywords: | Central charge c-vectors Harder-Narasimhan filtration maximal green sequences wide subcategories |
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