Abstract

Given a Tyurin degeneration of a Calabi—Yau manifold into a union of two quasi-Fano varieties, Doran—Harder—Thompson predicted that the Landau—Ginzburg mirrors of these two quasi-Fano varieties can be glued together to obtain the mirror of the Calabi—Yau variety equipped with a fibration structure over P^1. I will explain some generalizations of this conjecture and present a proof on the level of period integrals.