论文标题
Hyperkaehler歧管和相对Albanese中的复杂拉格朗日人
Complex Lagrangians in a hyperKaehler manifold and the relative Albanese
论文作者
论文摘要
令$ m $为HyperKähler歧管$ x $的复杂Lagrangian Submanifolds的模量空间，让$ \ varpi：\ wideHat {\ Mathcal {\ Mathcal {a}} \ rightArrow m $是$ m $的相对Albanese。我们证明$ \ wideHat {\ mathcal {a}} $具有天然的全态符号结构。投影$ \ varpi $定义了Sympletic歧管$ \ wideHat {\ Mathcal {a}} $的完全可集成的结构。特别是，相对于$ \ wideHat {\ Mathcal {a}} $上的sympletic形式，$ \ varpi $的光纤是复杂的拉格朗日。我们还证明了超过$ m $的相对PICARD的结果。
Let $M$ be the moduli space of complex Lagrangian submanifolds of a hyperKähler manifold $X$, and let $\varpi : \widehat{\mathcal{A}} \rightarrow M$ be the relative Albanese over $M$. We prove that $\widehat{\mathcal{A}}$ has a natural holomorphic symplectic structure. The projection $\varpi$ defines a completely integrable structure on the symplectic manifold $\widehat{\mathcal{A}}$. In particular, the fibers of $\varpi$ are complex Lagrangians with respect to the symplectic form on $\widehat{\mathcal{A}}$. We also prove analogous results for the relative Picard over $M$.
