Braid group actions on derived categories of coherent sheaves

Details Braid group actions on derived categories of coherent sheaves Braid group actions on derived categories of coherent sheaves

2000-01-07

arxiv.org/abs/math/0001043v2

Duke Math. Jour. 108 (2001), 37--108.

Mathematics

Algebraic Geometry

63 pages, 6 figures. Minor referees' changes for publication in Duke Math. Jour

Scientific paper

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 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.

Affiliated with

Also associated with

No associations

Rating

Braid group actions on derived categories of coherent sheaves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Braid group actions on derived categories of coherent sheaves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Braid group actions on derived categories of coherent sheaves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-186507