Kronecker模空间的环退化

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-09-03 DOI:10.1016/j.jalgebra.2025.08.015

E. Kalashnikov

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引用次数: 0

摘要

本文证明了以原始半标准表对为索引的Kronecker颤模空间的坐标环存在有限SAGBI基。这导致了Kronecker模空间的环向退化为正环变，这是将Grassmannian的环向退化推广到Gonciulea-Lakshmibai[13]构造的Gelfand-Cetlin多面体。简并环型的矩多面体可以描述为两个Gelfand-Cetlin多面体的交点。我们解释了什么时候这可以推广到来自匹配场的退化。

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A toric degeneration of Kronecker moduli spaces

In this paper, we show that there is a finite SAGBI basis of the coordinate ring of a Kronecker quiver moduli space, indexed by primitive semi-standard tableaux pairs. This induces a toric degeneration of the Kronecker moduli space to a normal toric variety, a generalization of the toric degeneration of the Grassmannian to the Gelfand–Cetlin polytope constructed by Gonciulea–Lakshmibai [13]. The moment polytope of the degenerate toric variety can be described as the intersection of two Gelfand–Cetlin polytopes. We explain when this can be generalized to degenerations coming from matching fields.

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.