Torus Fibrations of Calabi-Yau Hypersurfaces in Toric Varieties and Mirror Symmetry
Torus Fibrations of Calabi-Yau Hypersurfaces in Toric Varieties and Mirror Symmetry
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环曲面变体中 Calabi-Yau 超曲面的环面纤维和镜面对称
DOI：
10.1215/s0012-7094-00-10124-x
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
Ilia Zharkov
中科院分区：
文献类型：
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作者：
Ilia Zharkov
我们考虑正则的Calabi-Yau超曲面在$N$维光滑环面品种。在这样一个超曲面上，在大的复结构极限点的邻域内，我们构造了一个球面S^{N-1}$上的纤维化，它的类属纤维是环面T^{N-1}$。此外，对于某些单参数的家庭，这样的超曲面，我们表明，monodromy变换是由平移的$T^{N-1}$纤维化的一节。最后，我们构造了一个对偶纤维化，并提供了一些证据，它描述了镜像家庭。
We consider regular Calabi-Yau hypersurfaces in $N$-dimensional smooth toric varieties. On such a hypersurface in the neighborhood of the large complex structure limit point we construct a fibration over a sphere $S^{N-1}$ whose generic fibers are tori $T^{N-1}$. Also for certain one-parameter families of such hypersurfaces we show that the monodromy transformation is induced by a translation of the $T^{N-1}$ fibration by a section. Finally we construct a dual fibration and provide some evidence that it describes the mirror family.