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arXiv · 1301.7632

Minuscule Schubert Varieties and Mirror Symmetry

Makoto Miura
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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 ${\boldsymbol{\Sigma}}$ 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.

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Makoto Miura. 2013-01-31. Minuscule Schubert Varieties and Mirror Symmetry. https://doi.org/10.3842/sigma.2017.067

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