Compactifications of moduli spaces of K3 surfaces with a higher-order nonsymplectic automorphism
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909487614394368 |
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| author | Alexeev, Valery Deopurkar, Anand Han, Changho |
| author_facet | Alexeev, Valery Deopurkar, Anand Han, Changho |
| contents | We describe Baily-Borel, toroidal, and geometric -- using the KSBA stable pairs -- compactifications of some moduli spaces of K3 surfaces with a nonsymplectic automorphism of order $3$ and $4$ for which the fixed locus of the automorphism contains a curve of genus $\ge2$. For order $3$, we treat all the maximal-dimensional such families. We show that the toroidal and the KSBA compactifications in these cases admit simple descriptions in terms of certain $ADE$ root lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11256 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compactifications of moduli spaces of K3 surfaces with a higher-order nonsymplectic automorphism Alexeev, Valery Deopurkar, Anand Han, Changho Algebraic Geometry 14D22, 14J28 We describe Baily-Borel, toroidal, and geometric -- using the KSBA stable pairs -- compactifications of some moduli spaces of K3 surfaces with a nonsymplectic automorphism of order $3$ and $4$ for which the fixed locus of the automorphism contains a curve of genus $\ge2$. For order $3$, we treat all the maximal-dimensional such families. We show that the toroidal and the KSBA compactifications in these cases admit simple descriptions in terms of certain $ADE$ root lattices. |
| title | Compactifications of moduli spaces of K3 surfaces with a higher-order nonsymplectic automorphism |
| topic | Algebraic Geometry 14D22, 14J28 |
| url | https://arxiv.org/abs/2412.11256 |