Mirror symmetry for two parameter models. I
Mirror symmetry for two parameter models. I
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两个参数模型的镜像对称。
DOI：
10.1090/amsip/001/21
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
S. Yau
中科院分区：
文献类型：
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作者：
B. Greene;S. Yau
本文利用镜像对称性研究了若干个B 11= 2的Calabi-Yau流形的Kähler类参数的量子几何。我们的主要兴趣在于模空间的结构和奇异模型对应的轨迹。当有两个参数时，这种结构比迄今为止研究的各种单参数模型要丰富得多。我们描述的内在结构的点（紧化）模空间，对应于大复杂的结构或经典极限。瞬子展开是有趣的，因为一些瞬子属于具有连续参数的族。我们计算了汤川耦合及其展开的亏格为零的瞬子。利用Bershadsky等人的最新结果，我们还计算了亏格为1的瞬子的瞬子数。对于特定的参数值的模型成为双理性的某些模型与一个参数。因此，模空间的紧化因子包含单参数模型的模空间的副本。我们的讨论通过特定的模型P 4（1，1，2，2，2）[8]和P 4（1，1，2，2，6）[12]进行。另一个例子，P 4（1，1，1，6，9）[18]，有点不同，是一个配套文件的主题。
We study, by means of mirror symmetry, the quantum geometry of the Kähler-class parameters of a number of Calabi-Yau manifolds that have b 11= 2. Our main interest lies in the structure of the moduli space and in the loci corresponding to singular models. This structure is considerably richer when there are two parameters than in the various one-parameter models that have been studied hitherto. We describe the intrinsic structure of the point in the (compactification of the) moduli space that corresponds to the large complex structure or classical limit. The instanton expansions are of interest owing to the fact that some of the instantons belong to families with continuous parameters. We compute the Yukawa couplings and their expansions in terms of instantons of genus zero. By making use of recent results of Bershadsky et al. we compute also the instanton numbers for instantons of genus one. For particular values of the parameters the models become birational to certain models with one parameter. The compactification divisor of the moduli space thus contains copies of the moduli spaces of one-parameter models. Our discussion proceeds via the particular models P 4 (1, 1, 2, 2, 2)[8] and P 4 (1, 1, 2, 2, 6)[12]. Another example, P 4 (1, 1, 1, 6, 9)[18], that is somewhat different is the subject of a companion paper.