On the codimension 1 PGL(3) orbit closures in $\text{Gr}(3,6)$
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916861855137792 |
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| author | Choudhary, Tanav |
| author_facet | Choudhary, Tanav |
| contents | The projective linear group $\text{PGL}(3)$ naturally acts on the Grassmannian $\text{Gr}(3, V_2)$ of $3$-dimensional subspaces of the vector space $V_2$ of homogeneous conics in 3 variables. It was proved by Abdallah, Emsalem and Iarrobino in 2021 that this action has a one-parameter family of orbits along with 14 special orbits. The codimension 1 orbits of this action consist of the entire one-parameter family of orbits, along with 2 of the 14 special orbits. In this paper, we calculate the classes of the codimension 1 orbit closures in the Chow ring of $\text{Gr}(3, V_2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18608 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the codimension 1 PGL(3) orbit closures in $\text{Gr}(3,6)$ Choudhary, Tanav Algebraic Geometry The projective linear group $\text{PGL}(3)$ naturally acts on the Grassmannian $\text{Gr}(3, V_2)$ of $3$-dimensional subspaces of the vector space $V_2$ of homogeneous conics in 3 variables. It was proved by Abdallah, Emsalem and Iarrobino in 2021 that this action has a one-parameter family of orbits along with 14 special orbits. The codimension 1 orbits of this action consist of the entire one-parameter family of orbits, along with 2 of the 14 special orbits. In this paper, we calculate the classes of the codimension 1 orbit closures in the Chow ring of $\text{Gr}(3, V_2)$. |
| title | On the codimension 1 PGL(3) orbit closures in $\text{Gr}(3,6)$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2507.18608 |