Affine elliptic surfaces with type-A singularities and orbi-conifolds

Abstract

Following the work of Castano-Bernard and Matessi on conifold transition in the Gross-Siebert program, we construct orbi-conifold transitions of the Shoen's Calabi-Yau threefold and their mirrors. The construction glues together the local models for orbi-conifold transitions in the previous work with Kanazawa.

v2: some typos corrected. 38 pages, 18 figures

References in corpus (5)

• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Supersymmetric partition functions on Riemann surfaces
• Integral affine structures on spheres and torus fibrations of Calabi-Yau toric hypersurfaces I
• On the connectedness of the standard web of Calabi-Yau 3-folds and small transitions
• Degenerations and Lagrangian fibrations of Calabi-Yau manifolds