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Branes in the moduli space of framed sheaves. (English) Zbl 1396.14014
Branes in the moduli space of Higgs bundles provide a connection between the geometric Langland program and mirror symmetry. In this work the authors contribute to the study of branes in other types of varieties, namely, they present a systematic study of the existence of branes in Nakajima quiver varieties. In section 2 is presented an overview of the construction of Nakajima quiver varieties, fixing the terminology and objects that will be needed further in the work. In section 3, a systematic method to construct branes of all possible types on Nakajima quiver varieties is obtained, by describing several types of involutions on these varieties. Finally, in section 4, the methods presented in section 3 are used to produce examples of non-empty branes in the moduli spaces of framed torsion free sheaves on the projective plane, which are particular cases of Nakajima quiver varieties.

##### MSC:
 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) 32M10 Homogeneous complex manifolds 14H70 Relationships between algebraic curves and integrable systems 16G20 Representations of quivers and partially ordered sets 14D24 Geometric Langlands program (algebro-geometric aspects)
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