Equivariant Linearization and Rotation Domains on K3 Surfaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911218434834432 |
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| author | Iwasaki, Katsunori |
| author_facet | Iwasaki, Katsunori |
| contents | We construct a lot of K3 surface automorphisms of positive entropy having rotation domains of ranks 1 and 2. To carry out this construction, we first lay theoretical foundations concerning equivariant linearization of nonlinear maps under resolutions of quotient singularities, linear models near exceptional components, Salem numbers and multipliers at periodic points, two kinds of fixed point formulas and related indices at exceptional components. Then these basic tools are combined with the method of hypergeometric groups to enable us to detect various types of rotation domains on K3 surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16303 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant Linearization and Rotation Domains on K3 Surfaces Iwasaki, Katsunori Algebraic Geometry Dynamical Systems 14J28, 14J50, 11K16 We construct a lot of K3 surface automorphisms of positive entropy having rotation domains of ranks 1 and 2. To carry out this construction, we first lay theoretical foundations concerning equivariant linearization of nonlinear maps under resolutions of quotient singularities, linear models near exceptional components, Salem numbers and multipliers at periodic points, two kinds of fixed point formulas and related indices at exceptional components. Then these basic tools are combined with the method of hypergeometric groups to enable us to detect various types of rotation domains on K3 surfaces. |
| title | Equivariant Linearization and Rotation Domains on K3 Surfaces |
| topic | Algebraic Geometry Dynamical Systems 14J28, 14J50, 11K16 |
| url | https://arxiv.org/abs/2510.16303 |