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<p>We realise the Bott-Samelson resolutions of type A Schubert varieties as quiver Grassmannians. In order to explicitly describe this isomorphism, we introduce the notion of a <i>geometrically compatible</i> decomposition for any permutation in the symmetric group <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10468_2025_10356_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(S_n\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation>. For smooth type A Schubert varieties, we identify a suitable dimension vector such that the corresponding quiver Grassmannian is isomorphic to the Schubert variety. To obtain these isomorphisms, we construct a special quiver with relations and investigate two classes of quiver Grassmannians for this quiver.</p>

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Quiver Grassmannians for the Bott-Samelson Resolution of Type A Schubert Varieties

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  • 发表日期：

    2025年8月11日

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  • Giulia Iezzi

摘要

We realise the Bott-Samelson resolutions of type A Schubert varieties as quiver Grassmannians. In order to explicitly describe this isomorphism, we introduce the notion of a geometrically compatible decomposition for any permutation in the symmetric group \(S_n\) S n . For smooth type A Schubert varieties, we identify a suitable dimension vector such that the corresponding quiver Grassmannian is isomorphic to the Schubert variety. To obtain these isomorphisms, we construct a special quiver with relations and investigate two classes of quiver Grassmannians for this quiver.