Quiver Grassmannians associated to nilpotent cyclic representations defined by single matrix

Mateusz Lowiel

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arXiv · 2406.03970

Quiver Grassmannians associated to nilpotent cyclic representations defined by single matrix

Mateusz Lowiel

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Abstract

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.

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BibTeX RIS

Mateusz Lowiel. 2024-06-06. Quiver Grassmannians associated to nilpotent cyclic representations defined by single matrix. https://arxiv.org/abs/2406.03970

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