GKM-Theory for Torus Actions on Cyclic Quiver Grassmannians

2020/08/30 by Martina Lanini, Lanini, Martina, Alexander Pütz +1 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2008.13138

openalex publication_date 2020/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define and investigate algebraic torus actions on quiver Grassmannians for nilpotent representations of the equioriented cycle. Examples of such varieties are type \tt A flag varieties, their linear degenerations, finite dimensional approximations of the GL_n-affine flag variety and affine Grassmannian. We show that these quiver Grassmannians, equipped with our torus action, are GKM-varieties and that their moment graph admits a combinatorial description in terms of coefficients quiver of the underlying quiver representations. By adapting to our setting results by Gonzales, we are able to prove that moment graph techniques can be applied to construct module bases for the equivariant cohomology of the above quiver Grassmannians.

Cited by

• Equivariant cohomology of juggling varieties in rank one
• Some Lagrangian quiver Grassmannians for the equioriented cycle
• Regularity in Linear Degenerations of Flag Variety

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