Towards the Doran-Harder-Thompson conjecture via the Gross-Siebert program
Algebraic Geometry
2021-05-07 v1 Mathematical Physics
math.MP
Abstract
The Doran-Harder-Thompson "gluing/splitting" conjecture unifies mirror symmetry conjectures for Calabi-Yau and Fano varieties, relating fibration structures on Calabi-Yau varieties to the existence of certain types of degenerations on their mirrors. This was studied for the case of Calabi-Yau complete intersections in toric varieties by Doran, Kostiuk and You for the Hori-Vafa mirror construction. In this paper we prove one direction of the conjecture using a modified version of the Gross-Siebert program. This involves a careful study of the implications within tropical geometry and applying modern deformation theory for singular Calabi-Yau varieties.
Cite
@article{arxiv.2105.02617,
title = {Towards the Doran-Harder-Thompson conjecture via the Gross-Siebert program},
author = {Lawrence J. Barrott and Charles F. Doran},
journal= {arXiv preprint arXiv:2105.02617},
year = {2021}
}