Speaker：

Promit Kundu (ShanghaiTech University)

Time：

September 21, 2026, 3:00–4:00 pm

Title：

Fixed-Point Loci of Moduli Spaces of Sheaves on Toric Orbifolds

Abstract：

I will present a combinatorial description of torus-equivariant sheaves on smooth projective toric orbifolds and apply it to fixed loci in moduli spaces of stable torsion-free sheaves. The main new ingredient is a gluing formula for stacky (S)-families on general toric quotient charts, which simultaneously keeps track of torus weights and the fine gradings determined by local stabilizers.

For characteristic functions supported in one box on every maximal chart, the stacky data reduce to compatible multi filtrations. Together with a balanced generating sheaf, this permits an extension of Kool’s GIT method to modified Gieseker stability and gives a scheme-theoretic description of the corresponding fixed-locus components.

The talk will focus on the rank-one case, where the construction becomes explicit and leads to combinatorial generating functions. This example illustrates phenomena absent for ordinary toric varieties, particularly the contribution of stacky weights and fine gradings.

Biography：

Promit Kundu is a postdoctoral researcher at ShanghaiTech University. He received his PhD in Mathematics from the University of Kansas in 2021, after completing his M.Math. at the Indian Statistical Institute and his B.Sc. in Mathematics at Jadavpur University. His research concerns algebraic geometry, with a focus on moduli spaces of sheaves, Deligne–Mumford stacks, toric geometry, and enumerative invariants. His work has appeared in Mathematische Zeitschrift, Pure and Applied Mathematics Quarterly, and the European Journal of Mathematics.