The Doran-Harder-Thompson conjecture for toric complete intersections
Algebraic Geometry
2023-01-24 v3
Abstract
Given a Tyurin degeneration of a Calabi-Yau complete intersection in a toric variety, we prove gluing formulas relating the generalized functional invariants, periods, and -functions of the mirror Calabi-Yau family and those of the two mirror Landau-Ginzburg models. Our proof makes explicit the "gluing/splitting" of fibrations in the Doran-Harder-Thompson mirror conjecture. Our gluing formula implies an identity, obtained by composition with their respective mirror maps, that relates the absolute Gromov-Witten invariants for the Calabi-Yaus and relative Gromov-Witten invariants for the quasi-Fanos.
Cite
@article{arxiv.1910.11955,
title = {The Doran-Harder-Thompson conjecture for toric complete intersections},
author = {Charles F. Doran and Jordan Kostiuk and Fenglong You},
journal= {arXiv preprint arXiv:1910.11955},
year = {2023}
}
Comments
39 pages. Revised according to referees' comments. To appear in Advances in Mathematics