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CATEGORIES:Algebraic Geometry Seminar
SUMMARY:Noncommutative deformations of curves and spherica
l twists - Michael Wemyss (Edinburgh)
DTSTART;TZID=Europe/London:20130529T141500
DTEND;TZID=Europe/London:20130529T151500
UID:TALK43898AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/43898
DESCRIPTION:I will explain why\, when studying derived autoequ
ivalences of 3-folds\, it is\nnecessary to conside
r noncommutative deformations of curves. In the t
alk I will give a\nconstruction of a certain "nonc
ommutative twist" associated to any floppable curv
e that recovers\nthe flop-flop functor on the leve
l of the derived category. The idea is that the c
ommutative\ndeformation base is too small for the
homological algebra to work\, so we need to fatten
it by\nconsidering noncommutative directions. Th
is generalizes work of Seidel--Thomas and Toda who
\nconsidered the special case when the curve defor
ms in only one direction. \n\nI will try to expla
in why considering noncommutative deformations is
strictly necessary\, as I\nwill show that consider
ing only the commutative deformations does not giv
e a derived\nautoequivalence as one might hope. T
he talk will be based around one example\, where t
he\nbirational geometry of a certain 3-fold is con
trolled by the cusp in the quantum plane\, which i
s\na 9-dimensional self-injective algebra. This is
all based on joint work with Will Donovan.
LOCATION:MR 13\, CMS
CONTACT:Caucher Birkar
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