Stability conditions for contraction algebras
Forum of Mathematics, Sigma, Tome 10 (2022)
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This paper gives a description of the full space of Bridgeland stability conditions on the bounded derived category of a contraction algebra associated to a $3$-fold flop. The main result is that the stability manifold is the universal cover of a naturally associated hyperplane arrangement, which is known to be simplicial and in special cases is an ADE root system. There are four main corollaries: (1) a short proof of the faithfulness of pure braid group actions in both algebraic and geometric settings, the first that avoid normal forms; (2) a classification of tilting complexes in the derived category of a contraction algebra; (3) contractibility of the stability space associated to the flop; and (4) a new proof of the $K(\unicode{x3c0} \,,1)$-theorem in various finite settings, which includes ADE braid groups.
@article{10_1017_fms_2022_65,
author = {Jenny August and Michael Wemyss},
title = {Stability conditions for contraction algebras},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {10},
year = {2022},
doi = {10.1017/fms.2022.65},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.65/}
}
Jenny August; Michael Wemyss. Stability conditions for contraction algebras. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.65
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