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- W1776192598 abstract "In this paper, we introduce a new class of quiver varieties, recovering as special cases the cyclic and classical Nakajima quiver varieties. We show that the geometry of the new quiver varieties is closely linked to the representation theory of a suitable finitely-generated algebra $mathcal{P}$, which is self-injective if $Q$ is of ADE Dynkin type. The affine quiver variety, defined as GIT quotient, is shown to be isomorphic to the moduli space of representations of a finitely-generated algebra $mathcal{S}$. We construct a functor $Psi$ establishing a bijection between the strata of the affine quiver variety and the isomorphism classes of objects in proj $mathcal{P}$. Under $Psi$, the degeneration order between strata corresponds to Jensen--Su--Zimmermann's degeneration order on proj $mathcal{P}$. Furthermore, we use $Psi$ to realize the fibres of Nakajima's projection map $pi$ as quiver Grassmannians of $mathcal{P}$. The algebra $mathcal{P}$ specializes to the preprojective algebra if we consider classical quiver varieties. Finally, we use our results to construct desingularisations of quiver Grassmannians of modules of self-injective algebras of finite type." @default.
- W1776192598 created "2016-06-24" @default.
- W1776192598 creator A5050288308 @default.
- W1776192598 date "2014-05-19" @default.
- W1776192598 modified "2023-09-27" @default.
- W1776192598 title "Quiver varieties and self-injective algebras" @default.
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- W1776192598 hasPublicationYear "2014" @default.
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