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SUMMARY:Noncommutative deformations of curves and spherical twists - Micha
 el Wemyss (Edinburgh)
DTSTART:20130529T131500Z
DTEND:20130529T141500Z
UID:TALK43898@talks.cam.ac.uk
CONTACT:Caucher Birkar
DESCRIPTION:I will explain why\, when studying derived autoequivalences of
  3-folds\, it is\nnecessary to consider noncommutative deformations of cur
 ves.  In the talk I will give a\nconstruction of a certain "noncommutative
  twist" associated to any floppable curve that recovers\nthe flop-flop fun
 ctor on the level of the derived category.  The idea is that the commutati
 ve\ndeformation base is too small for the homological algebra to work\, so
  we need to fatten it by\nconsidering noncommutative directions.  This gen
 eralizes work of Seidel--Thomas and Toda who\nconsidered the special case 
 when the curve deforms in only one direction.  \n\nI will try to explain w
 hy considering noncommutative deformations is strictly necessary\, as I\nw
 ill show that considering only the commutative deformations does not give 
 a derived\nautoequivalence as one might hope.  The talk will be based arou
 nd one example\, where the\nbirational geometry of a certain 3-fold is con
 trolled by the cusp in the quantum plane\, which is\na 9-dimensional self-
 injective algebra. This is all based on joint work with Will Donovan.
LOCATION:MR 13\, CMS
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