Disk counting on toric varieties via tropical curves
Disk counting on toric varieties via tropical curves
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通过热带曲线计算复曲面品种的磁盘
DOI：
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发表时间：
2012
期刊：
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通讯作者：
T. Nishinou
中科院分区：
文献类型：
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作者：
T. Nishinou
在本文中，我们定义了两个数。一种是用带停止点的热带曲线计数来定义，另一种是在拉格朗日边界条件下的环系全纯盘的个数。这两条曲线都应该满足一些关联条件。我们证明这些数字是一致的。这些数可以看作是全纯盘的Gromov-Witten型不变量，它们与闭全纯曲线的计数数既有相似之处，也有不同之处。我们研究了它们的几个方面。
In this paper, we define two numbers. One is defined by counting tropical curves with a stop, and the other is the number of holomorphic disks in toric varieties with Lagrangian boundary condition. Both of these curves should satisfy some incidence conditions. We show that these numbers coincide. These numbers can be considered as Gromov-Witten type invariants for holomorphic disks, and they have similarities as well as differences to the counting numbers of closed holomorphic curves. We study several aspects of them.