Minuscule Schubert Varieties and Mirror Symmetry

Symmetry Integrability and Geometry-Methods and Applications

article

Makoto Miura¹ 

[1] Korea Institute for Advanced Study

关键词: Calabi–Yau;    mirror symmetry;    minuscule;    Schubert variety;    toric degeneration;   

DOI  :  10.3842/SIGMA.2017.067

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown