Curves in Calabi-Yau threefolds and topological quantum field theory
Curves in Calabi-Yau threefolds and topological quantum field theory
复制标题
卡拉比-丘三重曲线和拓扑量子场论
DOI：
10.1215/s0012-7094-04-12626-0
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发表时间：
2005
影响因子：
2.5
通讯作者：
R. Pandharipande
中科院分区：
文献类型：
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作者：
J. Bryan;R. Pandharipande
我们继续研究Calabi-Yau三重曲线的局部Gromov-Witten不变量。我们定义了局部理论的相对不变量，它产生了一个1+1维的TQFT在环Q[[t]]中取值。Q[[t]]上的相关Frobenius代数是半单的。因此，我们得到了局部不变量的结构结果。作为我们的结构公式的一个简单的结果，我们恢复了封闭的局部不变量的情况下，无论是目标亏格或度等于1。
We continue our study of the local Gromov-Witten invariants of curves in Calabi-Yau threefolds. We define relative invariants for the local theory which give rise to a 1+1-dimensional TQFT taking values in the ring Q[[t]]. The associated Frobenius algebra over Q[[t]] is semisimple. Consequently, we obtain a structure result for the local invariants. As an easy consequence of our structure formula, we recover the closed formulas for the local invariants in case either the target genus or the degree equals 1.