Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
144 tokens/sec
GPT-4o
8 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

The structure of the moduli of gauged maps from a smooth curve (2305.09632v1)

Published 16 May 2023 in math.AG

Abstract: For a reductive group $G$, Harder-Narasimhan theory gives a structure theorem for principal $G$ bundles on a smooth projective curve $C$. A bundle is either semistable, or it admits a canonical parabolic reduction whose associated Levi bundle is semistable. We extend this structure theorem by constructing a $\Theta$-stratification of the moduli stack of gauged maps from $C$ to a projective-over-affine $G$-variety $X$. The open stratum coincides with the previously studied moduli of Mundet semistable maps, and in special cases coincides with the moduli of stable quasi-maps. As an application of the stratification, we provide a formula for K-theoretic gauged Gromov-Witten invariants when $X$ is an arbitrary linear representation of $G$. This can be viewed as a generalization of the Verlinde formula for moduli spaces of decorated principal bundles. We establish our main technical results for smooth families of curves over an arbitrary Noetherian base. Our proof develops an infinite-dimensional analog of geometric invariant theory and applies the theory of optimization on degeneration fans.

Summary

We haven't generated a summary for this paper yet.