On Kummer‐like surfaces attached to singularity and modular forms

DOI10.1002/MANA.202100552zbMATH Open1527.14082arXiv2012.11954OpenAlexW3115436413MaRDI QIDQ6047366

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Publication date: 9 October 2023

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Abstract: We study a family of lattice polarized $K3$ surfaces which is an extension of the family of Kummer surfaces derived from principally polarized Abelian surfaces. Our family has two special properties. First, it is coming from a resolution of a simple $K3$ singularity. Second, it has a natural parametrization by Hermitian modular forms of four complex variables. In this paper, we show two results: (1) We determine the transcendental lattice and the N'eron-Severi lattice of a generic member of our family. (2) We give a detailed description of the double covering structure associated with our $K3$ surfaces.

Full work available at URL: https://arxiv.org/abs/2012.11954

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