On lattice-polarized K3 surfaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917116791226368 |
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| author | Alexeev, Valery Engel, Philip |
| author_facet | Alexeev, Valery Engel, Philip |
| contents | We propose modifications to the commonly used definitions of lattice-polarized and lattice-quasipolarized smooth K3 surfaces, collecting various versions of the definition, and determining the effects of these choices on the resulting moduli space. We fill a gap in the theory, by replacing Weyl chambers with the new notion of a ``small cone'': the true datum in the definition of lattice quasipolarized K3 surfaces. In addition, we describe the separated moduli stack and moduli space for lattice-polarized K3 surfaces with $ADE$ singularities, an important notion for applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22557 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On lattice-polarized K3 surfaces Alexeev, Valery Engel, Philip Algebraic Geometry 14J28, 14J10 We propose modifications to the commonly used definitions of lattice-polarized and lattice-quasipolarized smooth K3 surfaces, collecting various versions of the definition, and determining the effects of these choices on the resulting moduli space. We fill a gap in the theory, by replacing Weyl chambers with the new notion of a ``small cone'': the true datum in the definition of lattice quasipolarized K3 surfaces. In addition, we describe the separated moduli stack and moduli space for lattice-polarized K3 surfaces with $ADE$ singularities, an important notion for applications. |
| title | On lattice-polarized K3 surfaces |
| topic | Algebraic Geometry 14J28, 14J10 |
| url | https://arxiv.org/abs/2505.22557 |