Wall-Crossing in Genus Zero Landau-Ginzburg Theory
Wall-Crossing in Genus Zero Landau-Ginzburg Theory
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DOI：
10.1515/crelle-2015-0005
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发表时间：
2014-02
期刊：
影响因子：
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通讯作者：
Dustin Ross;Y. Ruan
中科院分区：
文献类型：
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作者：
Dustin Ross;Y. Ruan
本文研究了Fan-Farvis-Ruan最近引入的一类模空间的亏格零壁交叉。该族具有相对于正有理参数的墙和腔结构。对于费马拟齐次多项式W（不一定是Calabi-Yau型），我们研究与这些模空间相关的不变量的自然生成函数。我们的过壁公式通过表明它们都位于与W.对于任意小的参数，我们的生成函数的特殊化是一个超几何级数，称为大I函数，它决定了整个拉格朗日锥。作为一个特殊的情况下，我们的墙壁交叉，我们得到了一个新的几何解释的朗道-金兹伯格镜像定理。
We study genus zero wall-crossing for a family of moduli spaces introduced recently by Fan-Farvis-Ruan. The family has a wall and chamber structure relative to a positive rational parameter. For a Fermat quasi-homogeneous polynomial W (not necessarily Calabi-Yau type), we study natural generating functions of invariants associated to these moduli spaces. Our wall-crossing formula relates the generating functions by showing that they all lie on the same Lagrangian cone associated to the Fan-Jarvis-Ruan-Witten theory of W. For arbitrarily small parameter, a specialization of our generating function is a hypergeometric series called the big I-function which determines the entire Lagrangian cone. As a special case of our wall-crossing, we obtain a new geometric interpretation of the Landau-Ginzburg mirror theorem.