论文标题
通过圆环动作列举理性接触曲线
Enumeration of rational contact curves via torus actions
论文作者
论文摘要
我们证明，在任何触点复杂的射影空间中，与有理接触（Legendrian）曲线相关的某些Gromov-witten数字列出了列举。另外，我们在kontsevich空间上使用BOTT公式来找到这些数字的确切值。例如，计算了$ \ mathbb {p}^{3} $和$ \ mathbb {p}^{5} $中低度的有理接触曲线数量。结果与现有结果一致。
We prove that some Gromov-Witten numbers associated to rational contact (Legendrian) curves in any contact complex projective space with arbitrary incidence conditions are enumerative. Also, we use Bott formula on the Kontsevich space to find the exact value of those numbers. As an example, the numbers of rational contact curves of low degree in $\mathbb{P}^{3}$ and $\mathbb{P}^{5}$ are computed. The results are consistent with existing results.
