亚纯群作用与拉格朗日纤维化的支撑定理
Meromorphic Group Actions and the Support Theorem for Lagrangian Fibrations
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中文总结 AI 辅助
研究全纯辛复空间上拉格朗日纤维化，构造亚纯群的亚纯作用，结合霍奇理论方法证明相关支撑定理及紧凯勒空间同调自由性定理。
中文摘要 AI 辅助
我们在全空间是凯勒（但可能非紧或奇异）且基是复流形的假设下，证明了关于全纯辛复空间上拉格朗日纤维化的几个新结果。首先，我们构造了一族亚纯群的亚纯作用。其次，我们利用此结构以及霍奇理论方法，证明了拉格朗日纤维化的Ngô支撑定理的一个版本。在此过程中，我们证明了配备亚纯群作用的紧凯勒空间上同调的自由性定理。
英文摘要
We prove several new results about Lagrangian fibrations on holomorphic symplectic complex spaces, under the assumption that the total space is Kähler (but possibly non-compact or singular) and that the base is a complex manifold. First, we construct a meromorphic action by a family of meromorphic groups. Second, we use this structure, together with Hodge-theoretic methods, to prove a version of Ngô's support theorem for Lagrangian fibrations. Along the way, we prove a freeness theorem for the cohomology of compact Kähler spaces equipped with a meromorphic group action.
