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

TL;DR

This paper constructs and analyzes orbi-conifold transitions in Calabi-Yau threefolds and their mirrors, extending the Gross-Siebert program with new local models for singularity transitions.

Contribution

It introduces new local models for orbi-conifold transitions in Calabi-Yau threefolds, advancing the understanding of mirror symmetry and singularity transitions.

Findings

Construction of orbi-conifold transitions in Schoen's Calabi-Yau threefolds

Extension of local models for singularity transitions

Connections to mirror symmetry in the Gross-Siebert program

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.