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Seminario MALGA Padova Verona - Moduli Algebre Anelli

Mercoledi' 27 Febbraio 2013 - G. Cerulli Irelli, S. Scherotzke

ARGOMENTI: Seminari

Mercoledi' 27 Febbraio 2013 a Padova, in Aula 2BC45 della Torre Archimede si terra' il prossimo incontro del Seminario Padova - Verona MALGA (moduli, algebre, anelli).

ore 15:00
Giovanni Cerulli Irelli, Universita' di Bonn
"A functorial approach for the study of singularities of quiver Grasmmannians of Dynkin type"

-Abstract
Given a Dynkin quiver Q and a Q-representation M, a quiver Grassmannian X = Gre(M) is the projective variety of all subrepresentations of M of dimension vector e. This variety is not smooth in general, and its geometry is rather complicated. In particular it is useful to have a desingularization of X at our disposal. In this talk I will describe how to obtain such a desingularization. This is done by constructing an algebra BQ (which was newto us) with many interesting properties, e.g. it is derived equivalent to the Auslander algebra of kQ. To the Q-representation M it is hence associated a BQ-module ^M whose quiver Grassmannians gives the desired desingularization of X. This is joint work with Evgeny Feigin and Markus Reineke (arXiv: 1209.3960).


ore 16,30
Sarah Scherotzke, Universita' di Bonn
"Quiver varieties and Derived Categories"

-Abstract
Quiver varieties have been invented by Nakajima to give a geometric construction of representations of quantum groups. They have also been used recently to construct monodial categorifications of cluster algebras. 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. We will also establish the link between quiver varieties and the desingularisation map defined in Giovanni Cerulli-Irelli's talk. This is joint work with Bernhard Keller.

Rif. int. S. Bazzoni

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