New mirror pairs of Calabi-Yau orbifolds
Alan Stapledon

TL;DR
This paper establishes a new representation-theoretic approach to mirror symmetry, constructing infinite pairs of orbifolds with mirror Hodge diamonds and analyzing their properties, especially in the context of Fermat quintic and symmetric group actions.
Contribution
It introduces a novel representation-theoretic framework for Borisov-Batyrev mirror symmetry and constructs new orbifold pairs with mirror Hodge structures, extending mirror symmetry to orbifolds.
Findings
Constructed infinitely many orbifold pairs with mirror Hodge diamonds.
Proved the conjecture that orbifold Hodge diamonds are also mirror.
Identified smooth Calabi-Yau threefolds via $ ext{Hilb}$ schemes with explicit mirror Hodge data.
Abstract
We prove a representation-theoretic version of Borisov-Batyrev mirror symmetry, and use it to construct infinitely many new pairs of orbifolds with mirror Hodge diamonds, with respect to the usual Hodge structure on singular complex cohomology. We conjecture that the corresponding orbifold Hodge diamonds are also mirror. When is the Fermat quintic in , and is a -equivariant, toric resolution of its mirror , we deduce that for any subgroup of the alternating group , the -Hilbert schemes - and - are smooth Calabi-Yau threefolds with (explicitly computed) mirror Hodge diamonds.
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.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds
