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arXiv · 2509.19637

Stability and disconnected groups

Andres Fernandez Herrero·Andrés Ibáñez Núñez
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Abstract

We study the notion of semistability for principal bundles over curves with possibly disconnected reductive structure group. We establish a new characterization of the behavior of semistability under change of group, novel even in the connected case, and prove that all existing notions of semistability are equivalent, thus settling a question by Biswas-Gomez. The key ingredients for our results include a study of cocharacters and characters of disconnected linear algebraic groups, and an extension of the recursive description of Kirwan stratifications in Geometric Invariant Theory to the case of disconnected groups.

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Andres Fernandez Herrero, Andrés Ibáñez Núñez. 2025-09-23. Stability and disconnected groups. https://arxiv.org/abs/2509.19637

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