$\PGL$ orbits on products of flag varieties
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909418090659840 |
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| author | Coskun, Izzet Gündüz, Abuzer |
| author_facet | Coskun, Izzet Gündüz, Abuzer |
| contents | In this paper, we study the existence of a dense orbit for the diagonal $\PGL(n)$ action on self-products of partial flag varieties. We determine when there exists a dense orbit for flag varieties of the form $F(k_1, \dots, k_r; n)^m$ when $k_i = i$ or when $m=3$ and $k_i = \ell + i$ for some $\ell \geq 0$. We also show that certain infinite families of products do not have a dense orbit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04870 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\PGL$ orbits on products of flag varieties Coskun, Izzet Gündüz, Abuzer Algebraic Geometry 14L30, 14M15, 14M17, 14L35, 51N30 In this paper, we study the existence of a dense orbit for the diagonal $\PGL(n)$ action on self-products of partial flag varieties. We determine when there exists a dense orbit for flag varieties of the form $F(k_1, \dots, k_r; n)^m$ when $k_i = i$ or when $m=3$ and $k_i = \ell + i$ for some $\ell \geq 0$. We also show that certain infinite families of products do not have a dense orbit. |
| title | $\PGL$ orbits on products of flag varieties |
| topic | Algebraic Geometry 14L30, 14M15, 14M17, 14L35, 51N30 |
| url | https://arxiv.org/abs/2412.04870 |