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arXiv · 1910.11955

The Doran-Harder-Thompson conjecture for toric complete intersections

Charles F. Doran·Jordan Kostiuk·Fenglong You
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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 $I$-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.

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Charles F. Doran, Jordan Kostiuk, Fenglong You. 2019-10-25. The Doran-Harder-Thompson conjecture for toric complete intersections. https://arxiv.org/abs/1910.11955

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