On the $\mathrm{PGL}_2$-equivariant intersection theory of $\mathrm{Gr}(2,4)$
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915896644075520 |
|---|---|
| author | Sun, Yuxuan |
| author_facet | Sun, Yuxuan |
| contents | We determine the $\mathrm{PGL}_2$-equivariant Chow ring of $\mathrm{Gr}(2,4)^s$, the $\mathrm{PGL}_2$-stable locus of $\mathrm{Gr}(2,4)$, over any algebraically closed based field of characteristic not equal to 2 or 3. In the process, we demonstrate that the quotient stack $[\mathrm{Gr}(2,4)^s/\mathrm{PGL}_2]$ can be presented as the quotient of an open subset of $\mathbb{P}^1$ by a suitably chosen $S_4\leq \mathrm{PGL}_2$. We also discuss some apparent difficulties with computing the full $\mathrm{PGL}_2$-equivariant Chow ring of $\mathrm{Gr}(2,4)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27046 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the $\mathrm{PGL}_2$-equivariant intersection theory of $\mathrm{Gr}(2,4)$ Sun, Yuxuan Algebraic Geometry 14C15, 14C17 (Primary), 14D23, 14L24 (Secondary) We determine the $\mathrm{PGL}_2$-equivariant Chow ring of $\mathrm{Gr}(2,4)^s$, the $\mathrm{PGL}_2$-stable locus of $\mathrm{Gr}(2,4)$, over any algebraically closed based field of characteristic not equal to 2 or 3. In the process, we demonstrate that the quotient stack $[\mathrm{Gr}(2,4)^s/\mathrm{PGL}_2]$ can be presented as the quotient of an open subset of $\mathbb{P}^1$ by a suitably chosen $S_4\leq \mathrm{PGL}_2$. We also discuss some apparent difficulties with computing the full $\mathrm{PGL}_2$-equivariant Chow ring of $\mathrm{Gr}(2,4)$. |
| title | On the $\mathrm{PGL}_2$-equivariant intersection theory of $\mathrm{Gr}(2,4)$ |
| topic | Algebraic Geometry 14C15, 14C17 (Primary), 14D23, 14L24 (Secondary) |
| url | https://arxiv.org/abs/2603.27046 |