A toric degeneration of Kronecker moduli spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918136994856960 |
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| author | Kalashnikov, Elana |
| author_facet | Kalashnikov, Elana |
| contents | 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. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19961 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A toric degeneration of Kronecker moduli spaces Kalashnikov, Elana Algebraic Geometry 14D06, 13A50, 14L24 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. 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. |
| title | A toric degeneration of Kronecker moduli spaces |
| topic | Algebraic Geometry 14D06, 13A50, 14L24 |
| url | https://arxiv.org/abs/2410.19961 |