Mathematics > Representation Theory
arXiv:2507.13945 (math)
[Submitted on 18 Jul 2025 (v1), last revised 13 Jul 2026 (this version, v3)]
Abstract:Let $A$ be a gentle algebra. For every collection of string and band diagrammes, we consider the constructible subset of the variety of representations containing all modules with this underlying diagramme. We study degenerations of such sets. We show that these sets are defined by vectors of integers which we call $h$-vectors and which are related to a restricted version of the hom-order. We provide combinatorial criteria for the existence of a degeneration, involving the removal of an arrow or the resolving of a type of configuration called "reaching".
Submission history
From: Judith Marquardt [view email]
[v1]
Fri, 18 Jul 2025 14:15:08 UTC (1,645 KB)
[v2]
Mon, 19 Jan 2026 21:21:42 UTC (1,644 KB)
[v3]
Mon, 13 Jul 2026 08:56:55 UTC (1,898 KB)
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