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On the smooth locus in flat linear degenerations of flag varieties
Algebraic Combinatorics, Volume 9 (2026) no. 2, pp. 513-541

We use some moment graph techniques, recently introduced by Lanini and Pütz, to provide a description of $T$-fixed points in the smooth locus of flat linear degenerations of flag varieties, generalizing a result proved by Cerulli Irelli, Feigin and Reineke for the Feigin degeneration. Moreover, we propose a different combinatorial criterion linking the smoothness at a fixed point to transitive tournaments.

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Accepted:
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DOI: 10.5802/alco.477
Classification: 05E10, 14M15
Keywords: linear degenerations, quiver representations, quiver Grassmannians, torus actions, transitive tournaments
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Di Trani, Sabino. On the smooth locus in flat linear degenerations of flag varieties. Algebraic Combinatorics, Volume 9 (2026) no. 2, pp. 513-541. doi: 10.5802/alco.477
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