Minuscule Schubert Varieties and Mirror Symmetry
Minuscule Schubert Varieties and Mirror Symmetry
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DOI：
10.3842/sigma.2017.067
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发表时间：
2013-01
影响因子：
0.9
通讯作者：
Makoto Miura
中科院分区：
文献类型：
--
作者：
Makoto Miura
我们考虑极小Schubert簇中光滑的完全相交的Calabi-Yau 3-folds，并通过将周围Schubert簇退化为Hibi复曲面簇来研究它们的镜像对称性。我们列出了所有可能的这种类型的卡-丘3-折叠变形等价，并找到一个新的例子光滑卡-丘3-折叠皮卡德数1;一个完整的交叉在局部阶乘舒伯特簇${\boldsymbol{\Sigma}}$的凯莱平面${\mathbb{OP}}^2 $。我们计算了这个Calabi-Yau 3-fold的拓扑不变量和BPS数，并推测它有一个非平凡的Fourier-Mukai伙伴。
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.