Framed duality and mirror symmetry for toric complete intersections

TL;DR

This paper extends the concept of f-mirror symmetry from hypersurfaces to complete intersections in toric varieties, developing a duality framework that broadens mirror symmetry understanding and explores Landau-Ginzburg/Complete-Intersection correspondence.

Contribution

It generalizes framed duality and f-mirror symmetry to complete intersections, expanding previous hypersurface-focused results and analyzing mirror pairs of projective complete intersections.

Findings

Developed framed duality for complete intersections in toric varieties.

Strengthened results on hypersurfaces by extending to complete intersections.

Discussed a generalized LG/Complete-Intersection correspondence.

Abstract

This paper is devoted to systematically extend $f$-mirror symmetry between families of hypersurfaces in complete toric varieties, as introduced in \cite{R-fTV}, to families of complete intersections subvarieties. Namely, $f$-mirror symmetry is induced by framed duality of framed toric varieties extending Batyrev-Borisov polar duality between Fano toric varieties. Framed duality has been defined and essentially well described for families of hypersurfaces in toric varieties in the previous \cite{R-fTV}. Here it is developed for families of complete intersections, allowing us to strengthening some previous results on hypersurfaces. In particular, the class of projective complete intersections and their mirror partners are studied in detail. Moreover, a (generalized) Landau-Ginzburg/Complete-Intersection correspondence is discussed, extending to the complete intersection setup the LG/CY correspondence firstly studied Chiodo-Ruan and Krawitz.