Moduli of super-representations of quivers

Abstract

In this note, we construct moduli spaces of super-representations of quivers by extending King's Geometric Invariant Theory (GIT) framework to the super setting. Using the even part of super general linear groups and a parity-shifting operator, we construct moduli spaces that topologically parameterize super-representations of a fixed super-dimension. We also outline the construction of super quiver varieties for super-representations of framed quivers (without doubling); and realise super-Grassmannians and super-flag varieties as geometric quotients within this setting.

arXiv commentAdded a precise definition of "isomorphism classes'' of families in the context of the moduli functor in Section 5. A typo in the choice of stability parameter in section 6.1 corrected