Constructing special Lagrangian m-folds in C^m by evolving quadrics
Constructing special Lagrangian m-folds in C^m by evolving quadrics
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通过演化二次曲面在 C^m 中构造特殊的拉格朗日 m 折叠
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发表时间：
2000
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通讯作者：
D. joyce
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作者：
D. joyce
这是构造C^m中特殊拉格朗日子流形的显式例子的系列文章中的第二篇。第一篇论文是Math.DG/0008021，它研究了具有大对称群的特殊拉格朗日m-折叠。第三个是Math.DG/0010036，它利用本文的思想在C^3中构造了特殊的拉格朗日三重曲线族。
本文构造了C^m中特殊的拉格朗日m-折叠，它由C^m中的拉格朗日平面R^m中的二次流形的(m-1)-子流形构成，一般它们只有离散的对称群。我们的一些例子以前是由Lawler和Harvey使用不同的方法构造的。
这些论文的主要目的是为研究紧致特殊拉格朗日m-折叠在Calabi-Yau m-折叠中的奇性奠定基础。理解这样的奇点对于解决关于Calabi-Yau三折的镜面对称性的Syz猜想是很重要的。本文构造的特殊拉格朗日m-折叠包括S^a x S^b x S^1上的许多锥，其中a+b=m-2，这是Calabi-Yau m-折叠中特殊拉格朗日m-折叠奇点的局部模型。
This is the second in a series of papers constructing explicit examples of special Lagrangian submanifolds in C^m. The first paper was math.DG/0008021, which studied special Lagrangian m-folds with large symmetry groups. The third is math.DG/0010036, which uses ideas from this paper to construct families of special Lagrangian 3-folds in C^3.
This paper describes a construction of special Lagrangian m-folds in C^m which are fibred by (m-1)-submanifolds which are quadrics in Lagrangian planes R^m in C^m. Generically they have only discrete symmetry groups. Some of our examples have been previously constructed by Lawlor and Harvey, using different methods.
The principal motivation for these papers is to lay the foundations for the study of singularities of compact special Lagrangian m-folds in Calabi-Yau m-folds. Understanding such singularities will be important in resolving the SYZ conjecture on Mirror Symmetry of Calabi-Yau 3-folds. The special Lagrangian m-folds in C^m we construct here include many cones on S^a x S^b x S^1 for a+b=m-2, which are local models for singularities of special Lagrangian m-folds in Calabi-Yau m-folds.