Lattice Polarized K3 Surfaces and Siegel Modular Forms
Algebraic Geometry
2010-04-21 v1
Abstract
The goal of the present paper is two-fold. First, we present a classification of algebraic K3 surfaces polarized by the lattice H+E_8+E_7. Key ingredients for this classification are: a normal form for these lattice polarized K3 surfaces, a coarse moduli space and an explicit description of the inverse period map in terms of Siegel modular forms. Second, we give explicit formulas for a Hodge correspondence that relates these K3 surfaces to principally polarized abelian surfaces. The Hodge correspondence in question underlies a geometric two-isogeny of K3 surfaces.
Cite
@article{arxiv.1004.3503,
title = {Lattice Polarized K3 Surfaces and Siegel Modular Forms},
author = {Adrian Clingher and Charles F. Doran},
journal= {arXiv preprint arXiv:1004.3503},
year = {2010}
}