论文标题
对数符号几何形状中的混合霍奇结构
Mixed Hodge structures in log symplectic geometry
论文作者
论文摘要
我们研究具有纯重量的对数符号形式的SNC对数符号对（x，y）$的共同体环。我们表明，在某种自然条件下，$ x \ setminus y $的同时戒指展示了好奇的硬列施兹属性。显示出类似的结果，可用于与探测性不可还原性全态符号歧管相关的极限混合hodge结构。我们提供了几个纯重量的对数符合性对的示例，包括一类群集型品种，以及来自Feigin和Odesski的工作的示例。我们表明，投射不可还原性全态形态歧管的良好变性的中央纤维的成分产生对数symbletectic Pairs。
We study the cohomology rings of snc log symplectic pairs $(X,Y)$ which have log symplectic forms of pure weight. We show that under a certain natural condition, the cohomology ring of $X \setminus Y$ exhibits the curious hard Lefschetz property. Analogous results are shown to hold for limit mixed Hodge structures associated to good degenerations of projective irreducible holomorphic symplectic manifolds. We provide several examples of log symplectic pairs of pure weight including a class of cluster-type varieties, and examples coming from the work of Feigin and Odesski. We show that the components of the central fiber of good degenerations of projective irreducible holomorphic symplectic manifolds produce log symplectic pairs.
