Minuscule Schubert Varieties and Mirror Symmetry

Abstract

We consider smooth complete intersection Calabi-Yau 3-folds in minuscule Schubert varieties, and study their mirror symmetry by degenerating the ambient Schubert varieties to Hibi toric varieties. We list all possible Calabi-Yau 3-folds of this type up to deformation equivalences, and find a new example of smooth Calabi-Yau 3-folds of Picard number one; a complete intersection in a locally factorial Schubert variety $\mathbf{\Sigma }$ of the Cayley plane ${\mathbb{OP}}^2$. We calculate topological invariants and BPS numbers of this Calabi-Yau 3-fold and conjecture that it has a non-trivial Fourier-Mukai partner.

References in corpus (7)

• Homological projective duality for Grassmannians of lines
• Dual Pairs of Gauged Linear Sigma Models and Derived Equivalences of Calabi-Yau threefolds
• Higher genus Gromov-Witten invariants of the Grassmannian, and the Pfaffian Calabi-Yau threefolds
• Complete intersection Calabi--Yau manifolds with respect to homogeneous vector bundles on Grassmannians
• A pair of Calabi-Yau manifolds from a two parameter non-Abelian gauged linear sigma model
• Apéry constants of homogeneous varieties
• Gorenstein locus of minuscule Schubert varieties

Cited by in corpus (6)

• Dual Pairs of Gauged Linear Sigma Models and Derived Equivalences of Calabi-Yau threefolds
• A pair of Calabi-Yau manifolds from a two parameter non-Abelian gauged linear sigma model
• Degenerations and Lagrangian fibrations of Calabi-Yau manifolds
• Mirror Symmetry and Projective Geometry of Fourier-Mukai Partners
• Complete intersection Calabi--Yau threefolds in Hibi toric varieties and their smoothing
• Degenerating Hodge structure of one-parameter family of Calabi-Yau threefolds