Quiver Grassmannians associated to nilpotent cyclic representations defined by single matrix
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910474997596160 |
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| author | Lowiel, Mateusz |
| author_facet | Lowiel, Mateusz |
| contents | 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 $\mathbf{1}=(1,\dots,1)$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03970 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quiver Grassmannians associated to nilpotent cyclic representations defined by single matrix Lowiel, Mateusz Representation Theory Algebraic Geometry 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 $\mathbf{1}=(1,\dots,1)$, 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. |
| title | Quiver Grassmannians associated to nilpotent cyclic representations defined by single matrix |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2406.03970 |