On Calabi--Yau fractional complete intersections
Abstract
In this article, we study mirror symmetry for pairs of singular Calabi--Yau manifolds which are double covers of toric manifolds. Their period integrals can be seen as certain `fractional' analogues of those of ordinary complete intersections. This new structure can then be used to solve their Riemann--Hilbert problems. The latter can then be used to answer definitively questions about mirror symmetry for this class of Calabi--Yau manifolds.
Cite
@article{arxiv.2008.04039,
title = {On Calabi--Yau fractional complete intersections},
author = {Tsung-Ju Lee and Bong H. Lian and Shing-Tung Yau},
journal= {arXiv preprint arXiv:2008.04039},
year = {2022}
}
Comments
21 pages. Comments are welcome! In this version, we fix some statements: (1) the statement in Theorem 0.2 was too strong; our argument shows the dimension of the solution space is equal to the dimension of the relevant cohomology group; (2) Section 1.5 is slightly modified without significant changes: we fixed the argument in Remark 1.3; (3) Corollaries in Section 2.4 are re-ordered