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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2403.04544 |
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| _version_ | 1866914795325751296 |
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| author | Papazachariou, Thedoros S. |
| author_facet | Papazachariou, Thedoros S. |
| contents | We study the K-moduli space of products of Fano varieties in relation to the product of K-moduli spaces of the product components. We show that there exists a well-defined morphism from the product of K-moduli stacks of Fano varieties to the K-moduli stack of their product. Furthermore, we show that this morphism is an isomorphism if any two varieties with different irreducible components are non-isomorphic, and a torsor if they are. Our results rely on the theory of stacks and previous work by Zhuang.
We use our main result to obtain an explicit description of the K-moduli stack/ space of Fano threefolds with Picard rank greater than 6, along with a wall-crossing description, and a detailed polyhedral wall-crossing description for K-moduli of log Fano pairs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04544 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On products of K-moduli spaces Papazachariou, Thedoros S. Algebraic Geometry We study the K-moduli space of products of Fano varieties in relation to the product of K-moduli spaces of the product components. We show that there exists a well-defined morphism from the product of K-moduli stacks of Fano varieties to the K-moduli stack of their product. Furthermore, we show that this morphism is an isomorphism if any two varieties with different irreducible components are non-isomorphic, and a torsor if they are. Our results rely on the theory of stacks and previous work by Zhuang. We use our main result to obtain an explicit description of the K-moduli stack/ space of Fano threefolds with Picard rank greater than 6, along with a wall-crossing description, and a detailed polyhedral wall-crossing description for K-moduli of log Fano pairs. |
| title | On products of K-moduli spaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2403.04544 |