Equivalences of Families of Stacky Toric Calabi-Yau Hypersurfaces
Charles F. Doran, David Favero, and Tyler L. Kelly
TL;DR
This paper establishes derived equivalences between certain stacky hypersurfaces on different toric varieties, unifying mirror constructions and simplifying classifications of Calabi-Yau hypersurfaces.
Contribution
It introduces a method to derive equivalences between partial crepant resolutions of stacky hypersurfaces sharing the same anti-canonical system, linking various toric mirror constructions.
Findings
Derived equivalences between different stacky hypersurfaces
Unified toric mirror symmetry frameworks
Reduced Reid's classification to 81 families
Abstract
Given the same anti-canonical linear system on two distinct toric varieties, we provide a derived equivalence between partial crepant resolutions of the corresponding stacky hypersurfaces. The applications include: a derived unification of toric mirror constructions, calculations of Picard lattices for linear systems of quartic surfaces, and a birational reduction of Reid's list to 81 families.
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.