Stability and disconnected groups

2025/09/23 by Herrero, Andres Fernandez, Núñez, Andrés Ibáñez · 1 citation
#14D20 (Secondary) #14L17 (Primary) #14L24 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.19637

Abstract

We study the notion of semistability for principal bundles over curves with possibly disconnected structure group. We establish a new characterization of semistability under change of group which is novel even in the connected case. A key ingredient is our identification of the rational characters of any linear algebraic group with the Weyl-invariant rational characters of a maximal torus. In the reductive case, we prove an analogous statement for integral cocharacters. As an application, we extend the recursive description of Kirwan stratifications in Geometric Invariant Theory to disconnected groups, and use it in our study semistability for principal bundles.

Citations

• Intrinsic Donaldson-Thomas theory. I. Component lattices of stacks
• Refined Harder-Narasimhan filtrations in moduli theory
• Meromorphic Hodge moduli spaces for reductive groups in arbitrary characteristic
• The structure of the moduli of gauged maps from a smooth curve
• Stability conditions in geometric invariant theory
• On the structure of instability in moduli theory
• On the stack of semistable G-bundles over an elliptic curve
• Good moduli spaces for Artin stacks

Cited by

• Multiplicative dimensional reduction

Related

• Semistable Principal Bundles-II (in positive characteristics)
• Semistable reduction for G-bundles on curves
• Extension of structure groups of principal bundles in positive characteristic
• Rationality of the instability parabolic and related results
• Strongly Semistable Bundles on a Curve over a finite field