| Orateur(s) | Sarah SCHEROTZKE - Oxford et IMJ,
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| Titre | Graded quiver varieties and derived categories |
| Date | 23/05/2013 |
| Horaire | 10:30 à 11:30 |
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| Diffusion | |
| Résume | Graded quiver varieties were invented by Nakajima to give a geometric construction of representations of quantum groups. They have also been used recently to construct monoidal categorifications of cluster algebras. Graded quiver varieties associated with a quiver Q are defined by geometric invariant theory. In my talk, I will explain how they can be described explicitly as modules of certain mesh categories. We show that there is a bijection between their strata and the isomorphism classes of objects in the derived category of the quiver Q. Under this bijection the degeneration order between strata corresponds to a degeneration order defined on the derived category by Jensen-Su-Zimmermann. Furthermore, we describe the fibers of the desingularisation map from the smooth quiver variety to the affine quiver variety as Grassmanianns of a representable functor of the derived category of Q. This is joint work with Bernhard Keller. |
| Salle | 11 rue Pierre et Marie Curie - 75005 Paris |
| Adresse | |
