Degenerations and Lagrangian fibrations of Calabi-Yau manifolds
arXiv:1801.02749
Abstract
We discuss various topics on degenerations and special Lagrangian torus fibrations of Calabi-Yau manifolds in the context of mirror symmetry. A particular emphasis is on Tyurin degenerations and the Doran-Harder-Thompson conjecture, which builds a bridge between mirror symmetry for Calabi-Yau manifolds and that for quasi-Fano manifolds. The proof of the conjecture is of interest in its own right and leads us to a few other related topics such as SYZ mirror symmetry, theta functions and geometric quantization. Inspired by the conjecture, we also propose a new construction of Landau-Ginzburg models by splitting Calabi-Yau fibrations.
fixed some typos, changed the title, 55 pages, 8 figures, Handbook for Mirror Symmetries of Calabi-Yau and Fano Manifolds
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