Families of Calabi–Yau hypersurfaces in Q-Fano toric varieties
Families of Calabi–Yau hypersurfaces in Q-Fano toric varieties
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Q-Fano 复曲面变体中的 Calabi-Yau 超曲面家族
DOI：
10.1016/j.matpur.2016.02.012
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Robin Guilbot
中科院分区：
文献类型：
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作者：
M. Artebani;Paola Comparin;Robin Guilbot
给出了Q-Fano复曲面簇中的一般超曲面是Calabi-Yau簇的一个充分条件。此外，我们还定义了Berglund-Hübsch-Krawitz构造的推广，即当环境是一个具有挠自由类群的Q-Fano复曲面簇，且定义的多项式不一定是Delsarte型时.最后，我们引入了族之间的对偶的Calabi-Yau超曲面，其中包括Batyrev和Berglund-Hübsch-Krawitz镜像结构。这是根据多面体对Δ 1 <$Δ 2之间的极对偶给出的，其中Δ 1和Δ 2 <$是正则的。
We provide a sufficient condition for a general hypersurface in a Q-Fano toric variety to be a Calabi–Yau variety in terms of its Newton polytope. Moreover, we define a generalization of the Berglund–Hübsch–Krawitz construction in case the ambient is a Q-Fano toric variety with torsion free class group and the defining polynomial is not necessarily of Delsarte type. Finally, we introduce a duality between families of Calabi–Yau hypersurfaces which includes both Batyrev and Berglund–Hübsch–Krawitz mirror constructions. This is given in terms of a polar duality between pairs of polytopes Δ 1⊆ Δ 2, where Δ 1 and Δ 2⁎ are canonical.