Compact moduli of Calabi-Yau cones and Sasaki-Einstein spaces
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909284959256576 |
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| author | Odaka, Yuji |
| author_facet | Odaka, Yuji |
| contents | We construct proper moduli algebraic spaces of K-polystable $\mathbb{Q}$-Fano cones (a.k.a. Calabi-Yau cones) or equivalently their links i.e., Sasaki-Einstein manifolds with singularities.
As a byproduct, it gives alternative algebraic construction of proper K-moduli of $\mathbb{Q}$-Fano varieties. In contrast to the previous algebraic proof of its properness ([BHLLX, LXZ]), we do not use the $δ$-invariants ([FO, BJ]) nor the $L^2$-normalized Donaldson-Futaki invariants. We use the local normalized volume of [Li] and the higher $Θ$-stable reduction instead. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compact moduli of Calabi-Yau cones and Sasaki-Einstein spaces Odaka, Yuji Algebraic Geometry High Energy Physics - Theory Commutative Algebra Differential Geometry We construct proper moduli algebraic spaces of K-polystable $\mathbb{Q}$-Fano cones (a.k.a. Calabi-Yau cones) or equivalently their links i.e., Sasaki-Einstein manifolds with singularities. As a byproduct, it gives alternative algebraic construction of proper K-moduli of $\mathbb{Q}$-Fano varieties. In contrast to the previous algebraic proof of its properness ([BHLLX, LXZ]), we do not use the $δ$-invariants ([FO, BJ]) nor the $L^2$-normalized Donaldson-Futaki invariants. We use the local normalized volume of [Li] and the higher $Θ$-stable reduction instead. |
| title | Compact moduli of Calabi-Yau cones and Sasaki-Einstein spaces |
| topic | Algebraic Geometry High Energy Physics - Theory Commutative Algebra Differential Geometry |
| url | https://arxiv.org/abs/2405.07939 |