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September 29, 2025Open Access

Skeletal Torus Actions and GKM Structures on Quiver Grassmannians of String Representations

Key Points

The study classifies quiver Grassmannians of string representations, highlighting their GKM-variety structure.
Key properties include cellular decomposition and a torus action with finitely many fixed points and one-dimensional orbits.
Focusing on equioriented type A and nilpotent equioriented type quiver representations, the analysis provides insight on skeletal actions.
GKM-varieties exhibit unique torus actions crucial for understanding quiver representations in geometry.

Abstract

Quiver Grassmannians of equioriented type A and nilpotent equioriented type A quiver representations are GKM-varieties. In particular, they have a cellular decomposition and admit a torus action with finitely many fixed points and one-dimensional orbits (i. e. skeletal action). We examine the case of string representations and provide a classification of all corresponding quiver Grassmannians with a GKM-variety structure.

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Cite This Study

Alexander Pütz (Tue,) studied this question.

synapsesocial.com/papers/68da58c9c1728099cfd10954 https://doi.org/https://doi.org/10.48550/arxiv.2503.08233

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