Some Mirror partners with Complex multiplication
Jan Christian Rohde
TL;DR
This paper constructs examples of Calabi-Yau 3-manifolds and their mirror families over Shimura varieties, highlighting dense sets of complex multiplication fibers with implications in theoretical physics.
Contribution
It provides explicit examples of Calabi-Yau families over Shimura varieties with mirror subfamilies also over Shimura varieties, illustrating dense CM fibers.
Findings
Families contain dense CM fibers.
Mirror subfamilies also over Shimura varieties.
Relevance to theoretical physics via Gukov and Vafa's work.
Abstract
In this note we provide examples of families of Calabi-Yau 3-manifolds over Shimura varieties, whose mirror families contain subfamilies over Shimura varieties. Therefore these original families and subfamilies on the mirror side contain dense sets of complex multiplication fibers. In view of the work of S. Gukov and C. Vafa this is of special interest in theoretical physics.
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 · Geometry and complex manifolds · Advanced Algebra and Geometry