Equivariant cohomology of juggling varieties in rank one

2025/11/04 by Bidhan Paul, Paul, Bidhan
#14M15 #16G20 #55N91 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2511.02585

Abstract

We determine the ring structure of the torus-equivariant cohomology of rank-one juggling varieties with rational coefficients. By realizing these varieties as cyclic quiver Grassmannians, we construct a Knutson--Tao type basis for their equivariant cohomology. Using this basis, we give an explicit description of the ring structure in terms of generators and relations, and compute the corresponding structure constants. Finally, we show that these structure constants are integral.

Citations

• Type A algebraic coherence conjecture of Pappas and Rapoport
• Laumon parahoric local models via quiver Grassmannians
• Generalized juggling patterns, quiver Grassmannians and affine flag varieties
• Permutation actions on Quiver Grassmannians for the equioriented cycle via GKM-Theory
• GKM-Theory for Torus Actions on Cyclic Quiver Grassmannians
• Geometry of Quiver Grassmannians of Dynkin type with applications to cluster algebras
• Local models of Shimura varieties, I. Geometry and combinatorics
• Permutation representations on Schubert varieties
• An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson
• Nearby cycles for local models of some Shimura varieties
• On the flatness of models of certain Shimura varieties of PEL-type

Related

• Equivariant structure constants for ordinary and weighted projective space
• Equivariant cohomology for cyclic groups
• Formal Group Rings of Toric Varieties
• Structure Constants in equivariant oriented cohomology of flag varieties
• Localization of equivariant cohomology rings of real Grassmannians