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Stability conditions for contraction algebras

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  • Jenny August
  • ,
  • Michael Wemyss, University of Glasgow

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 Formula Presented-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 Formula Presented associated to the flop; and (4) a new proof of the Formula Presented-theorem in various finite settings, which includes ADE braid groups.

TidsskriftForum of Mathematics, Sigma
StatusUdgivet - sep. 2022

Bibliografisk note

Funding Information:
During the research on this paper, J.A. was supported by the Carnegie Trust for the Universities of Scotland, and M.W. was supported by EPSRC grants EP/R009325/1 and EP/R034826/1. J.A. further acknowledges support from the Max Planck Institute for Mathematics and a DNRF Chair from the Danish National Research Foundation (grant no. DNRF156).

Publisher Copyright:
© The Author(s), 2022. Published by Cambridge University Press.

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