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arXiv · 1210.5993

On Schubert decompositions of quiver Grassmannians

Oliver Lorscheid
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Abstract

In this paper, we introduce Schubert decompositions for quiver Grassmannians and investigate example classes of quiver Grassmannians with a Schubert decomposition into affine spaces. The main theorem puts the cells of a Schubert decomposition into relation to the cells of a certain simpler quiver Grassmannian. This allows us to extend known examples of Schubert decompositions into affine spaces to a larger class of quiver Grassmannians. This includes exceptional representations of the Kronecker quiver as well as representations of forests with block matrices of the form $\begin{pmatrix} 0&1\\ 0&0 \end{pmatrix}$. Finally, we draw conclusions on the Euler characteristics and the cohomology of quiver Grassmannians.

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Oliver Lorscheid. 2013-03-28. On Schubert decompositions of quiver Grassmannians. https://arxiv.org/abs/1210.5993

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