Mathematics – Algebraic Geometry
Scientific paper
2009-10-14
Mathematics
Algebraic Geometry
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.
Brav Christopher
Thomas Helmuth
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