Mirror symmetry for Pfaffian Calabi-Yau 3-folds via conifold transitions

Abstract

In this note we construct conifold transitions between several Calabi-Yau threefolds given by Pfaffians in weighted projective spaces and Calabi-Yau threefolds appearing as complete intersections in toric varieties. We use the obtained results to predict mirrors following ideas of \cite{BCKS, Batsmalltoricdegen}. In particular we consider the family of Calabi--Yau threefolds of degree 25 in ${\mathbb{P}}^9$ obtained as a transverse intersection of two Grassmannians in their Plucker embeddings.

11 pages, minor changes

References in corpus (2)

• Canonical Coordinates in Toric Degenerations
• Geometric transitions between Calabi-Yau threefolds related to Kustin-Miller unprojections

Cited by in corpus (4)

• Notes on nonabelian (0,2) theories and dualities
• Derived equivalent Hilbert schemes of points on K3 surfaces which are not birational
• Complete intersection Calabi--Yau manifolds with respect to homogeneous vector bundles on Grassmannians
• Calabi-Yau fibrations, simple K-equivalence and mutations