Techniques of computations of Dolbeault cohomology of solvmanifolds
Techniques of computations of Dolbeault cohomology of solvmanifolds
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DOI：
10.1007/s00209-012-1013-0
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发表时间：
2011-07
影响因子：
0.8
通讯作者：
H. Kasuya
中科院分区：
文献类型：
--
作者：
H. Kasuya
本文考虑具有格Γ使得N是具有左不变复结构的幂零李群的半直积。利用直积李代数的Dolbeaut上同调，计算了G/Γ上全纯线丛的直和的Dolbeaut上同调.作为这个计算的一个推论，我们可以利用有限维上链复形计算G/Γ的Dolbeault上同调Hp，q（G/Γ）.计算一些例子，我们观察到的Dolbeault上同调不同的选择格Γ。
We consider semi-direct productsof Lie groups with lattices Γ such thatNare nilpotent Lie groups with left-invariant complex structures. We compute the Dolbeault cohomology of direct sums of holomorphic line bundles overG/Γ by using the Dolbeaut cohomology of the Lie algebras of the direct product. As a corollary of this computation, we can compute the Dolbeault cohomologyHp,q(G/Γ) ofG/Γ by using a finite dimensional cochain complexes. Computing some examples, we observe that the Dolbeault cohomology varies for choices of lattices Γ.