We introduce the notion of log R-maps, and develop a proper moduli stack of stable log R-maps in the case of a hybrid gauged linear sigma model. Two virtual cycles (canonical and reduced) are constructed for these moduli stacks. The main results are two comparison theorems relating the reduced virtual cycle to the cosection localized virtual cycle, as well as the reduced virtual cycle to the canonical virtual cycle. This sets the foundation of a new technique for computing higher genus Gromov–Witten invariants of complete intersections.

中文翻译：

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对数标度线性西格玛模型

我们介绍了对数R-映射的概念，并在混合计量线性sigma模型的情况下，开发了稳定的对数R-映射的适当模堆栈。为这些模堆构造了两个虚拟周期（规范周期和简化周期）。主要结果是两个比较定理，它们将简化的虚拟循环与切面局部虚拟循环相关联，以及简化的虚拟循环与规范虚拟循环相关联。这就为计算完整交集的高属Gromov–Witten不变量奠定了新技术的基础。