Moduli of Multi-Uniformized Stacks and Seifert $\mathbb{G}_m^d$-Bundles
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908427007033344 |
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| author | Pan, Zhengkai |
| author_facet | Pan, Zhengkai |
| contents | We introduce multi-uniformized stacks as a generalization of the Abramovich--Hassett construction of uniformized twisted varieties. We prove an equivalence between the category of multi $\mathbb{Q}$-line bundles satisfying an analogue of Kollár's condition and the category of multi-uniformized twisted varieties, and we construct the corresponding moduli space. We then broaden the framework to encompass Kollár's Seifert $\mathbb{G}_m^d$-bundles, showing that their moduli likewise coincide with those of $d$-uniformized $d$-cyclotomic orbispaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22573 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moduli of Multi-Uniformized Stacks and Seifert $\mathbb{G}_m^d$-Bundles Pan, Zhengkai Algebraic Geometry We introduce multi-uniformized stacks as a generalization of the Abramovich--Hassett construction of uniformized twisted varieties. We prove an equivalence between the category of multi $\mathbb{Q}$-line bundles satisfying an analogue of Kollár's condition and the category of multi-uniformized twisted varieties, and we construct the corresponding moduli space. We then broaden the framework to encompass Kollár's Seifert $\mathbb{G}_m^d$-bundles, showing that their moduli likewise coincide with those of $d$-uniformized $d$-cyclotomic orbispaces. |
| title | Moduli of Multi-Uniformized Stacks and Seifert $\mathbb{G}_m^d$-Bundles |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2506.22573 |