Normal forms for Kummer surfaces

Abstract

We determine normal forms for the Kummer surfaces associated with abelian surfaces of polarization of type $(1,1)$, $(1,2)$, $(2,2)$, $(2,4)$, and $(1,4)$. Explicit formulas for coordinates and moduli parameters in terms of Theta functions of genus two are also given. The normal forms in question are closely connected to the generalized Riemann identities for Theta functions of Mumford's.

49 pages

References in corpus (3)

• K3 surfaces, modular forms, and non-geometric heterotic compactifications
• The Satake sextic in elliptic fibrations on K3
• Six line configurations and string dualities

Cited by in corpus (5)

• On isogenies among certain abelian surfaces
• On K3 surfaces of Picard rank 14
• On the mixed-twist construction and monodromy of associated Picard-Fuchs systems
• On the duality of F-theory and the CHL string in seven dimensions
• Geometry of Prym varieties for special bielliptic curves of genus three and five