Quiver Grassmannians for the Bott-Samelson resolution of type A Schubert varieties

2025/02/17 by Giulia Iezzi, Iezzi, Giulia · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics

paper · doi:10.48550/arxiv.2502.11790

Abstract

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 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.

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• Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials

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