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.
Huybrechts, Fourier--Mukai Transforms in Algebraic Geometry, Oxford Mathematical Monographs, Oxford University Press, Oxford
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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.