Foldable fans, cscK surfaces and local K-moduli
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866918151020609536 |
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| author | Tipler, Carl |
| author_facet | Tipler, Carl |
| contents | We study the moduli space of constant scalar curvature Kähler surfaces around the toric ones. To this aim, we introduce the class of foldable surfaces : smooth toric surfaces whose lattice automorphism group contain a non trivial cyclic subgroup. We classify such surfaces and show that they all admit a constant scalar curvature Kähler metric (cscK metric). We then study the moduli space of polarised cscK surfaces around a point given by a foldable surface, and show that it is locally modeled on a finite quotient of a toric affine variety with terminal singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01159 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Foldable fans, cscK surfaces and local K-moduli Tipler, Carl Algebraic Geometry Differential Geometry 14D22 (Primary) 53C25, 14J10, 14M25 (Secondary) We study the moduli space of constant scalar curvature Kähler surfaces around the toric ones. To this aim, we introduce the class of foldable surfaces : smooth toric surfaces whose lattice automorphism group contain a non trivial cyclic subgroup. We classify such surfaces and show that they all admit a constant scalar curvature Kähler metric (cscK metric). We then study the moduli space of polarised cscK surfaces around a point given by a foldable surface, and show that it is locally modeled on a finite quotient of a toric affine variety with terminal singularities. |
| title | Foldable fans, cscK surfaces and local K-moduli |
| topic | Algebraic Geometry Differential Geometry 14D22 (Primary) 53C25, 14J10, 14M25 (Secondary) |
| url | https://arxiv.org/abs/2402.01159 |