Braid group actions on derived categories of coherent sheaves

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dc.creatorSeidel, Paul
dc.creatorThomas, R. P.
dc.date2000-01-07
dc.date2000-08-30
dc.date.accessioned2026-07-07T04:33:15Z
dc.date.available2026-07-07T04:33:15Z
dc.descriptionThis 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 braid group actions arising from crepant resolutions of various singularities. Relations with the McKay correspondence and with exceptional sheaves on Fano manifolds are given. Moreover, the case of an elliptic curve is worked out in some detail.
dc.description63 pages, 6 figures. Minor referees' changes for publication in Duke Math. Jour
dc.identifierhttps://arxiv.org/abs/math/0001043
dc.identifierhttp://arxiv.org/abs/math/0001043
dc.identifierDuke Math. Jour. 108 (2001), 37--108.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58504
dc.subjectAlgebraic Geometry
dc.subjectHigh Energy Physics - Theory
dc.subjectSymplectic Geometry
dc.subject14J32; 18E30 ; 53D40; 20F36
dc.titleBraid group actions on derived categories of coherent sheaves
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