The Satake sextic in elliptic fibrations on K3

Abstract

We describe explicit formulas relevant to the F-theory/heterotic string duality that reconstruct from a specific Jacobian elliptic fibration on the Shioda-Inose surface covering a generic Kummer surface the corresponding genus-two curve using the level-two Satake coordinate functions. We derive explicitly the rational map on the moduli space of genus-two curves realizing the algebraic correspondence between a sextic curve and its Satake sextic. We will prove that it is not the original sextic defining the genus-two curve, but its corresponding Satake sextic which is manifest in the F-theory model, dual to the $\mathfrak{so}(32)$ heterotic string with an unbroken $\mathfrak{so}(28)\oplus \mathfrak{su}(2)$ gauge algebra.

23 pages

References in corpus (2)

• K3 surfaces, modular forms, and non-geometric heterotic compactifications
• Theta functions and algebraic curves with automorphisms

Cited by in corpus (20)

• Six line configurations and string dualities
• Nongeometric heterotic strings and dual F-theory with enhanced gauge groups
• Unbroken $E_7\times E_7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals
• A Universal Genus-Two Curve from Siegel Modular Forms
• The duality between F-theory and the Heterotic String in $D=8$ with two Wilson lines
• Kummer sandwiches and Greene-Plesser construction
• On isogenies among certain abelian surfaces
• Non-Geometric Vacua of the $\text{Spin}(32)/{\mathbb{Z}}_2$ Heterotic String and Little String Theories
• Machine learning for moduli space of genus two curves and an application to isogeny based cryptography
• Normal forms for Kummer surfaces
• On K3 surfaces of Picard rank 14
• Isogenous components of Jacobian surfaces
• On the mixed-twist construction and monodromy of associated Picard-Fuchs systems
• Genus Two Quasi-Siegel Modular Forms and Gromov-Witten Theory of Toric Calabi-Yau Threefolds
• On Néron-Severi lattices of Jacobian elliptic K3 surfaces
• On the duality of F-theory and the CHL string in seven dimensions
• Bezoutians and the discriminant of a certain quadrinomials
• Isogenies of certain K3 surfaces of rank 18
• The weighted moduli spaces of sextics
• Eight-dimensional non-geometric heterotic strings and enhanced gauge groups