For crepant resolutions X(1,3,9) and X(1,3,13) the derived categories admit faithful braid twist group actions of types D and E induced by spherical object configurations.
Quiver braid group action for a 3-fold crepant resolution
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abstract
The 3-fold cyclic quotient singularity denoted $\tfrac{1}{7}(1,2,4)$ admits a crepant resolution X with three exceptional Hirzebruch surfaces intersecting pairwise along curves. We show that the derived category D(X) carries a faithful action of a quiver braid group, where the relevant quiver is a 3-cycle encoding the intersection data.
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2026 1verdicts
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Some faithful algebraic braid twist group actions for 3-fold crepant resolutions
For crepant resolutions X(1,3,9) and X(1,3,13) the derived categories admit faithful braid twist group actions of types D and E induced by spherical object configurations.