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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.06662 |
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| _version_ | 1866913308454420480 |
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| author | Gaviria, Walter Páez |
| author_facet | Gaviria, Walter Páez |
| contents | We consider a moduli space of lattice polarized K3 surfaces with the additional information of a frame of the trascendental cohomology with respect to the lattice polarization. This moduli space is proved to be quasi-affine, and the existence of vector fields on it, called modular vector fields, is proved. A purely algebraic version of the algebra of Siegel quasi-modular forms is obtained as the algebra of global regular functions over this moduli space, with a differential structure coming from the modular vector fields. By means of trascendental considerations we are able to obtain a differential algebra of meromorphic Siegel quasi-modular forms from the previous algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modular Vector Fields for Lattice Polarized K3 Gaviria, Walter Páez Algebraic Geometry Complex Variables 11F11, 14C30, 14J28, 11F46 We consider a moduli space of lattice polarized K3 surfaces with the additional information of a frame of the trascendental cohomology with respect to the lattice polarization. This moduli space is proved to be quasi-affine, and the existence of vector fields on it, called modular vector fields, is proved. A purely algebraic version of the algebra of Siegel quasi-modular forms is obtained as the algebra of global regular functions over this moduli space, with a differential structure coming from the modular vector fields. By means of trascendental considerations we are able to obtain a differential algebra of meromorphic Siegel quasi-modular forms from the previous algebra. |
| title | Modular Vector Fields for Lattice Polarized K3 |
| topic | Algebraic Geometry Complex Variables 11F11, 14C30, 14J28, 11F46 |
| url | https://arxiv.org/abs/2404.06662 |