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arXiv · 2105.02617

Towards the Doran-Harder-Thompson conjecture via the Gross-Siebert program

Lawrence J. Barrott·Charles F. Doran
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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.

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BibTeXRIS

Lawrence J. Barrott, Charles F. Doran. 2021-05-06. Towards the Doran-Harder-Thompson conjecture via the Gross-Siebert program. https://arxiv.org/abs/2105.02617

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