2024/06/06 by Mateusz Lowiel, Lowiel, Mateusz
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2406.03970
openalex publication_date 2024/06/06 · openalex created_date 2024/06/08 · openalex updated_date 2026/07/28
In the present paper we study the geometry of the closed Białynicki-Birula cells of the quiver Grassmannians associated to a nilpotent representation of a cyclic quiver defined by a single matrix. For the special case, where we choose subrepresentations of dimension 1=(1,…,1), the main result of this paper is that the closed Białynicki-Birula cells are smooth. We also discuss the multiplicative structure of the cohomology ring of such spaces. Namely, we describe the so-called Knutson-Tao basis in context to the basis of equivariant cohomology that is dual to fundamental classes in equivariant homology.