surface $S_{[2 \hspace{1mm} 0 \hspace{1mm} 2]}$ in Appendix \[secA\].

Special points in the moduli of eight-dimensional non-geometric heterotic strings and F-theory duals with enhanced gauge groups {#sec3}
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Summary {#ssec3.1}
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There are finitely many points in the moduli of eight-dimensional non-geometric heterotic strings with unbroken $\mathfrak{e}_7\mathfrak{e}_7$ algebra, at which the non-Abelian gauge groups on the F-theory side are enhanced to rank 18.

In Section \[ssec3.2\], we show that the heterotic strings at these special points in the moduli can be described as deformations of the stable degenerations, as a result of the coincident 7-branes on the F-theory side. This effect can be seen as the insertion of 5-branes in the heterotic language. We also discuss applications to $SO(32)$ heterotic strings.

As stated in Section \[ssec2.3\], K3 surfaces become extremal on the F-theory side at these points in the moduli. The complex structures of the extremal K3 surfaces were classified in [@SZ], and using this result, the complex structures of the extremal K3 surfaces at these points in the moduli can be determined. This enables us to determine the Weierstrass equations of the extremal K3 surfaces that appear as compactification spaces on the F-theory side in the moduli. By using 