K3 SURFACES AND ORTHOGONAL MODULAR FORMS
Abstract We determine explicit generators for the ring of modular forms associated with the moduli spaces of K3 surfaces with automorphism group $(\mathbb {Z}/2\mathbb {Z})^2$ and of Picard rank 13 and higher. The K3 surfaces in question carry a canonical Jacobian elliptic fibration and the modular form generators appear as coefficients in the Weierstrass-type equations describing these fibrations.
Authors
- Andreas Malmendier (ORCID: https://orcid.org/0000-0002-5900-7384)
- Brandon Williams (ORCID: https://orcid.org/0000-0001-7599-6058)
- Adrian Clingher (ORCID: https://orcid.org/0000-0002-5369-7994)
Institutions
- Utah State University (US)
- University of Missouri–St. Louis (US)
- Heidelberg University (DE)
Publication Details
- Journal
- Nagoya Mathematical Journal
- Published
- 2025-08-29
- DOI
- https://doi.org/10.1017/nmj.2025.10071
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Simons Foundation