Hypergeometric equations and weighted projective spaces
Hypergeometric equations and weighted projective spaces
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超几何方程和加权射影空间
DOI：
10.1007/s11425-011-4218-5
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
V. Golyshev
中科院分区：
文献类型：
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作者：
A. Corti;V. Golyshev
我们计算了Hodge结构$\mathbb{V} = gr_{n - 1}^W R^{n- 1} f_！\mathbb{Z}$的Landau-Ginzburg模型f：Y → Y的镜像对偶到一个加权的射影空间W <$n的反正则锥的Reid的年龄函数的一个变体。这意味着，例如，w n有正则奇点当且仅当hn− 1，0$\mathbb {V} = 1$。本文给出了一般超几何变分的Hodge数的一个代数公式，证明了Landau-Ginzburg模型的一般纤维对Calabi-Yau簇是双有理的当且仅当W的一般反正则截面是Calabi-Yau簇.我们分析了104个具有正则奇点的加权3-空间，并证明了在Landau-Ginzburg模型的一般纤维是科代拉维为1的椭圆曲面的9种情况下，一般反正则截面不是K3曲面。
We compute the Hodge numbers of the polarised (pure) variation of Hodge structure $\mathbb{V} = gr_{n - 1}^W R^{n - 1} f_! \mathbb{Z}$ of the Landau-Ginzburg model f: Y → ℂ mirror-dual to a weighted projective space wℙn in terms of a variant of Reid’s age function of the anticanonical cone over wℙn. This implies, for instance, that wℙn has canonical singularities if and only if hn−1,0$\mathbb{V} = 1$. We state a conjectural formula for the Hodge numbers of general hypergeometric variations.We show that a general fibre of the Landau-Ginzburg model is birational to a Calabi-Yau variety if and only if a general anticanonical section of wℙ is Calabi-Yau. We analyse the 104 weighted 3-spaces with canonical singularities, and show that a general anticanonical section is not a K3 surface exactly in those 9 cases where a generic fibre of the Landau-Ginzburg model is an elliptic surface of Kodaira dimension 1.