The Laurent deformation conjecture for Tyurin-degenerate Calabi–Yau hypersurfaces

Let the central Hirzebruch scroll be the limiting member of the deformation family of Hirzebruch scrolls described above, and let its Calabi–Yau hypersurface be Tyurin-degenerate, while the corresponding hypersurfaces in the generic Hirzebruch scrolls admit regular smoothing deformations. Laurent deformation conjecture. The Laurent deformations of the Calabi–Yau hypersurface in the central Hirzebruch scroll are $\e\<\to0$ limit-images of the regular smoothing deformations in the Calabi–Yau hypersurface within the generic Hirzebruch scrolls. This proposes that Laurent deformations capture the limiting behavior of regular smoothings across the degeneration from generic to central Hirzebruch scrolls; the supplied text does not state whether the claim has been proved or disproved.