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Toric varieties and cluster algebras

Posted in
Speaker: 
G. Koshevoy
Affiliation: 
Russian Acad. of Sciences/MPI
Date: 
Thu, 2012-04-26 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

We associate a toric variety to the cluster algebra of the coordinate  ring of GL_n/P
(P is a parabolic subgroup). If such a cluster algebra is finite, then we have a smooth
toric variety.  Our conjecture is that this holds in general.To confirm this conjecture
we construct a smooth toric variety for a  framed acyclic quiver and study relations
between these two constructions of toric varieties.
 

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