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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2511.03885 |
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| _version_ | 1866911250993119232 |
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| author | Henestroza, Joaquin Torres |
| author_facet | Henestroza, Joaquin Torres |
| contents | Following the ideas of Bossinger and Fang, Fourier, and Littelman, we study iterated sequences for the Grassmannian $\operatorname{Gr} (3, n)$ as a special class of birational sequences. For each iterated sequence $S$, there is a weighting matrix $M_{S}$ corresponding to a valuation on the rational coordinate ring and we show that the initial form of a Plücker relation $\operatorname{in}_{M_S} (R_{I,J} )$ is binomial. We show that, in some cases, the cones $C_S$ in the tropical Grassmannian that satisfy $\operatorname{in}_{M_S} (\mathcal{I}_{3,n}) = \operatorname{in}_{C_S} (\mathcal{I}_{3,n})$ only depend on the first two indices used in each iteration. In the case of $\operatorname{Gr} (3, 6)$, these cones are obtained computationally and are classified up to automorphism induced by the symmetric group $S_6$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03885 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Birational sequences for the Grassmannian Gr(3,n) Henestroza, Joaquin Torres Algebraic Geometry Following the ideas of Bossinger and Fang, Fourier, and Littelman, we study iterated sequences for the Grassmannian $\operatorname{Gr} (3, n)$ as a special class of birational sequences. For each iterated sequence $S$, there is a weighting matrix $M_{S}$ corresponding to a valuation on the rational coordinate ring and we show that the initial form of a Plücker relation $\operatorname{in}_{M_S} (R_{I,J} )$ is binomial. We show that, in some cases, the cones $C_S$ in the tropical Grassmannian that satisfy $\operatorname{in}_{M_S} (\mathcal{I}_{3,n}) = \operatorname{in}_{C_S} (\mathcal{I}_{3,n})$ only depend on the first two indices used in each iteration. In the case of $\operatorname{Gr} (3, 6)$, these cones are obtained computationally and are classified up to automorphism induced by the symmetric group $S_6$. |
| title | Birational sequences for the Grassmannian Gr(3,n) |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2511.03885 |