The Satake sextic in F-theory

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 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 manifested in the F-theory model, dual to the so(32) heterotic string with an unbroken so(28) circle plus su(2) gauge algebra. (C) 2017 Elsevier B.V. All rights reserved.