Existence of moduli spaces for algebraic stacks
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866913240351506432 |
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| author | Alper, Jarod Halpern-Leistner, Daniel Heinloth, Jochen |
| author_facet | Alper, Jarod Halpern-Leistner, Daniel Heinloth, Jochen |
| contents | We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space and prove a semistable reduction theorem for points of algebraic stacks equipped with a $Θ$-stratification. These results provide a generalization of the Keel--Mori theorem to moduli problems whose objects have positive dimensional automorphism groups and give criteria on the moduli problem to have a separated or proper good moduli space. To illustrate our method, we apply these results to construct proper moduli spaces parameterizing semistable $\mathcal{G}$-bundles on curves and moduli spaces for objects in abelian categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1812_01128 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Existence of moduli spaces for algebraic stacks Alper, Jarod Halpern-Leistner, Daniel Heinloth, Jochen Algebraic Geometry 14D23, 14D22, 14H60, 18E15 We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space and prove a semistable reduction theorem for points of algebraic stacks equipped with a $Θ$-stratification. These results provide a generalization of the Keel--Mori theorem to moduli problems whose objects have positive dimensional automorphism groups and give criteria on the moduli problem to have a separated or proper good moduli space. To illustrate our method, we apply these results to construct proper moduli spaces parameterizing semistable $\mathcal{G}$-bundles on curves and moduli spaces for objects in abelian categories. |
| title | Existence of moduli spaces for algebraic stacks |
| topic | Algebraic Geometry 14D23, 14D22, 14H60, 18E15 |
| url | https://arxiv.org/abs/1812.01128 |