Lattice polarized K3 surfaces and Siegel modular forms

By Adrian Clingher, Charles F. Doran. 2010

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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 as follows: 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, the details of which are described by the authors in Clingher and Doran (2011)  [7] .

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/49220615c191e31ae9ec315ed1d18420ac2fc0b6