A Generalized Construction of Calabi-Yau Models and Mirror Symmetry
Per Berglund, Tristan Hubsch
TL;DR
This paper generalizes the construction of Calabi-Yau manifolds and mirror symmetry to include hypersurfaces in non-Fano toric varieties using Laurent polynomials, broadening the scope of mirror model pairs.
Contribution
It introduces a new method for constructing Calabi-Yau models via non-reflexive polytopes, extending Batyrev's framework to non-Fano cases with novel mirror pairs.
Findings
Constructed Calabi-Yau hypersurfaces in Hirzebruch n-folds for n=3,4
Developed a generalized approach using Laurent polynomials
Provided examples of new mirror pairs in non-Fano settings
Abstract
We extend the construction of Calabi-Yau manifolds to hypersurfaces in non-Fano toric varieties, requiring the use of certain Laurent defining polynomials, and explore the phases of the corresponding gauged linear sigma models. The associated non-reflexive and non-convex polytopes provide a generalization of Batyrev's original work, allowing us to construct novel pairs of mirror models. We showcase our proposal for this generalization by examining Calabi-Yau hypersurfaces in Hirzebruch n-folds, focusing on n=3,4 sequences, and outline the more general class of so-defined geometries.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.