In 2011, S. Cherkis introduced a class of manifolds via hyperkähler reductions, called bow varieties, starting from a generalization of quivers called bows. In 2017, H. Nakajima and Y. Takayama initiated the algebro-geometric study of these spaces by providing the so-called quiver description of bow varieties for the affine type A case. The aim of this seminar is to present a quiver description for bow varieties of any types and demonstrate their relationship with Nakajima’s quiver varieties. Specifically, we will begin by briefly recalling the construction of Nakajima’s quiver varieties via GIT. Then, we will introduce the notion of bow in relation quivers and brane systems. Hence, we will present the quiver description of bow varieties, illustrating some basic examples. Finally, we will recover Nakajima’s quiver varieties as a special class of bow varieties.

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