  The moduli in a 4D N=1 heterotic compactification on an elliptic CY, as well
as in the dual F-theoretic compactification, break into "base" parameters which
are even (under the natural involution of the elliptic curves), and "fiber" or
twisting parameters; the latter include a continuous part which is odd, as well
as a discrete part. We interpret all the heterotic moduli in terms of
cohomology groups of the spectral covers, and identify them with the
corresponding F-theoretic moduli in a certain stable degeneration. The argument
is based on the comparison of three geometric objects: the spectral and cameral
covers and the ADE del Pezzo fibrations. For the continuous part of the
twisting moduli, this amounts to an isomorphism between certain abelian
varieties: the connected component of the heterotic Prym variety (a modified
Jacobian) and the F-theoretic intermediate Jacobian. The comparison of the
discrete part generalizes the matching of heterotic 5brane / F-theoretic 3brane
impurities.
