Braid group actions on derived categories of coherent sheaves

  title={Braid group actions on derived categories of coherent sheaves},
  author={Paul Seidel and Richard P. Thomas},
  journal={Duke Mathematical Journal},
This paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety $X$. The motivation for this is Kontsevich's homological mirror conjecture, together with the occurrence of certain braid group actions in symplectic geometry. One of the main results is that when $\dim X \geq 2$, our braid group actions are always faithful. We describe conjectural mirror symmetries between smoothings and resolutions of singularities that lead us to find examples of… 

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