Λ-modules and holomorphic Lie algebroid connections
Λ-modules and holomorphic Lie algebroid connections
复制标题
Λ 模和全纯李代数体连接
DOI：
10.2478/s11533-012-0065-z
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发表时间：
2012
影响因子：
--
通讯作者：
Pietro Tortella
中科院分区：
文献类型：
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作者：
Pietro Tortella
设X是复光滑射影簇，G是X上的局部自由层.我们证明了对（Λ，λ）和对（L，λ）之间存在一一对应，其中Λ是X上满足Simpson公理的几乎多项式滤子代数的层，$ \equiv：Gr\Lambda \to Sym \bullet _{\mathcal{O}_X } \mathcal{G}$是同构，L是$\mathcal{G}$上的全纯李代数体结构，λ是F 1H 2（L，λ）中的一类，F 1H 2（L，λ）是L的第二上同调的第一Hodge滤子片.作为应用，我们构造了任意全纯李代数体L的半稳定平坦L-联络的模空间.这些的特殊例子是由广义全纯丛的任何广义复杂的结构相关联的全纯泊松流形。
Let X be a complex smooth projective variety, and G a locally free sheaf on X. We show that there is a one-to-one correspondence between pairs (Λ, Ξ), where Λ is a sheaf of almost polynomial filtered algebras over X satisfying Simpson’s axioms and $ \equiv :Gr\Lambda \to Sym \bullet _{\mathcal{O}_X } \mathcal{G}$ is an isomorphism, and pairs (L, Σ), where L is a holomorphic Lie algebroid structure on $\mathcal{G}$ and Σ is a class in F1H2(L, ℂ), the first Hodge filtration piece of the second cohomology of L.As an application, we construct moduli spaces of semistable flat L-connections for any holomorphic Lie algebroid L. Particular examples of these are given by generalized holomorphic bundles for any generalized complex structure associated to a holomorphic Poisson manifold.