Minuscule Schubert Varieties and Mirror Symmetry

Makoto Miura

Symmetry, integrability and geometry: methods and applications, Tome 13 (2017)

Résumé

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.

Détail

Keywords: Calabi–Yau; mirror symmetry; minuscule; Schubert variety; toric degeneration.

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