Braid groups and Kleinian singularities

Mathematics – Algebraic Geometry

Scientific paper

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Section 4 from versions 1 and 2 has been deleted due to an error in the proof of Theorem 2. Renamed the paper and rewrote the

Scientific paper

We establish faithfulness of braid group actions generated by twists along an
ADE configuration of $2$-spherical objects in a derived category. Our major
tool is the Garside structure on braid groups of type ADE. This faithfulness
result provides the missing ingredient in Bridgeland's description of a space
of stability conditions associated to a Kleinian singularity.

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