  In this work we study the duality between F-theory and the heterotic string
beyond the stable degeneration limit in F-theory and large fiber limit in the
heterotic theory. Building upon a recent proposal by Clingher-Doran and
Malmendier-Morrison, which phrases the duality on the heterotic side for a
particular class of models in terms of (fibered) genus two curves as
non-geometric heterotic compactifications - we establish the precise limit to
the semi-classical heterotic string in both eight and lower space-time
dimensions. In particular for six dimensional theories, we argue that this
class of non-geometric heterotic compactifications capture alpha'-quantum
corrections to the semi-classical heterotic supergravity compactifications on
elliptically fibered K3 surfaces. From the non-geometric heterotic theory, the
semi-classical phase on the K3 surface is recovered from a remarkable limit of
genus two Siegel modular forms combined with a geometric surgery operation.
Finally, in four dimensions we analyze another limit deep in the quantum regime
of the non-geometric heterotic string, which we refer to as the heterotic Sen
limit. In this limit we can explicitly argue that the semi-classical two-staged
fibrational structure of the heterotic hypermultiplet moduli space - recently
established by Alexandrov, Louis, Pioline and Valandro - gets corrected by
quantum effects.
