AI 中文总结
该研究证明了Gorsky等人引入的椭圆曲线带标记希格斯丛模空间相关的五类同构均为全纯辛同构，涉及仿射 Dynkin 型及对应循环群的希尔伯特概型。
AI 中文摘要
Gorsky、Nekrasov与Rubtsov引入了椭圆曲线E上带标记希格斯丛的模空间，并将其与余切丛上的点希尔伯特概型等同。后续Groechenig针对带标记有理曲线构造了四个类似同构，对应仿射 Dynkin 型$\tilde D_4$、$\tilde E_6$、$\tilde E_7$、$\tilde E_8$，适用于阶$|\Gamma|\in\{2,3,4,6\}$的循环群$\Gamma$对应的$T^*E$的$\Gamma$-希尔伯特概型。我们证明这五类情形下的同构均为全纯辛同构。
英文摘要
Gorsky, Nekrasov, and Rubtsov introduced the moduli space of marked Higgs bundles over an elliptic curve $E$ and identified it with the Hilbert scheme of points on the cotangent bundle. Later, Groechenig constructed four analogous isomorphisms on marked rational curves, of affine Dynkin types $\widetilde D_4$, $\widetilde E_6$, $\widetilde E_7$, and $\widetilde E_8$, for the $Γ$-Hilbert schemes of $T^*E$ for cyclic groups $Γ$ with $|Γ|\in\{2,3,4,6\}$. We prove that the isomorphisms in all five cases are holomorphic symplectomorphisms.
Comments20 pages, Comments welcome
