论文标题
$ \ mathbb {p}^1 $的旋转gromov-witten/hurwitz通信
The Spin Gromov-Witten/Hurwitz correspondence for $\mathbb{P}^1$
论文作者
论文摘要
我们研究$ \ mathbb {p}^1 $的旋转gromov-witten（GW）理论。使用$ \ mathbb {p}^1 $上的标准圆环动作，我们证明可以通过操作员形式主义表示相关的epivariant电位，并满足2-BKP的层次结构。由于这个结果，我们证明了Okounkov-Pandharipande的GW/Hurwitz对应的旋转类似物，以$ \ Mathbb {p}^1 $，这是由J. Lee猜想的。最后，我们证明，通用目标自旋曲线的这种对应关系遵循的构想变性公式，用于旋转GW不变性，该公式在虚拟维度0中保持。
We study the spin Gromov-Witten (GW) theory of $\mathbb{P}^1$. Using the standard torus action on $\mathbb{P}^1$, we prove that the associated equivariant potential can be expressed by means of operator formalism and satisfies the 2-BKP hierarchy. As a consequence of this result, we prove the spin analogue of the GW/Hurwitz correspondence of Okounkov-Pandharipande for $\mathbb{P}^1$, which was conjectured by J. Lee. Finally, we prove that this correspondence for a general target spin curve follows from a conjectural degeneration formula for spin GW invariants that holds in virtual dimension 0.
