论文标题
关于全体形态符号歧管的代数共截相的亚截骨
On algebraically coisotropic submanifolds of holomorphic symplectic manifolds
论文作者
论文摘要
我们研究了全体形状符号射击歧管$ m $中的代数共同体submanifolds $ x $。受到高度表面案例的结果的激励，我们提出了以下问题：当$ x $不含糊不清时，确实是，$（x，m）$是$（z \ times y，n \ times y）$（x，m）$是$ n，$ n，y $ y $ holomorphic simplectic symplectic and $ z \ sexset n lagrangian是lagrangian？我们证明，当$ m $是亚洲的品种时，确实是这种情况，并且当规范捆绑包$ k_x $是半ample时给出一些部分答案。特别是，当$ k_x $是nef and big时，$ x $是$ m $的拉格朗日（实际上，这也没有nefness假设）。我们还指出，与$ M $不可约Hyperkähler相比，拉格朗日亚曼菲尔德并不存在于足够普通的亚伯利亚品种中。
We investigate algebraically coisotropic submanifolds $X$ in a holomorphic symplectic projective manifold $M$. Motivated by our results in the hypersurface case, we raise the following question: when $X$ is not uniruled, is it true that up to a finite étale cover, the pair $(X,M)$ is a product $(Z\times Y, N\times Y)$ where $N, Y$ are holomorphic symplectic and $Z\subset N$ is Lagrangian? We prove that this is indeed the case when $M$ is an abelian variety, and give some partial answer when the canonical bundle $K_X$ is semi-ample. In particular, when $K_X$ is nef and big, $X$ is Lagrangian in $M$ (in fact this also holds without nefness assumption). We also remark that Lagrangian submanifolds do not exist on a sufficiently general Abelian variety, in contrast to the case when $M$ is irreducible hyperkähler.
