On Kummer-like surfaces attached to singularity and modular forms
Algebraic Geometry
2023-06-13 v4 Complex Variables
Abstract
We study a family of lattice polarized 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 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 surfaces.
Cite
@article{arxiv.2012.11954,
title = {On Kummer-like surfaces attached to singularity and modular forms},
author = {Atsuhira Nagano and Hironori Shiga},
journal= {arXiv preprint arXiv:2012.11954},
year = {2023}
}
Comments
22 pages, 11 figures ; typos are corrected; references are renewed