arXiv subjects

Umesh Dubey

Publications and source records attributed to Umesh Dubey.

3 recordsLinked to original sources

arXiv2026

Moduli of super-representations of quivers

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.

math.RT↗

arXiv2021

Moduli of parabolic sheaves and filtered Kronecker modules

We give functorial moduli construction of pure parabolic sheaves, in the sense of Alvarez-Consul and A. King, using the moduli of filtered Kronecker modules we introduced in our earlier work. We also use a version of S. G. Langton's result due to K. Yokogawa to deduce the projectivity of moduli of pure parabolic sheaves of maximal dimension. As an application of functorial moduli construction, we can get the morphisms at the level of moduli stacks.

math.AG↗

arXiv2019

Moduli of filtered quiver representations

In this paper, we give a construction of the moduli space of filtered representations of a given quiver of fixed dimension vector with the appropriate notion of stability. The construction of the moduli of filtered representations uses the moduli of representations of ladder quiver. The ladder quiver is introduced using a given quiver and a linear type quiver. We also study determinantal theta functions on such moduli spaces.

math.AG↗