The Doran-Harder-Thompson conjecture on mirror fibrations

Let $\frX \to \AA^1$ be a Tyurin degeneration to $\frZ_0 \cup_{\frD} \frZ_1$, with mirror Calabi-Yau $\widecheck{\frX_{gen}}$ and mirror divisor $\frD$. A Tyurin degeneration is a one-parameter degeneration whose central fibre is a simple normal crossings divisor with smallest strata of codimension one. Doran-Harder-Thompson conjecture on mirror fibrations. The mirror $\widecheck{\frX_{gen}}$ admits a map to $\PP^1$ with fibres smooth Calabi-Yau varieties of one dimension lower, and $\frD$ is mirror to a generic fibre of this fibration. The statement gives one direction of the Doran-Harder-Thompson conjecture; in the source it is presented as a corollary proved under a compatible toric degeneration, while the broader conjectural picture concerns fibrations arising from Tyurin degenerations.