复结构变形障碍与上同调收缩
Obstructions of deforming complex structures and cohomology contractions
AI总结：
本文从分析角度改进了Kodaira原理，通过幂级数方法和弗洛里切尔谱序列，揭示了复结构变形障碍与上同调收缩映射的关系，并给出了具有平凡canonical包的紧复流形的新无障碍准则。
摘要：
Kodaira原理指出，适当的上同调收缩映射会消去复结构变形的障碍。在本文中，我们从纯分析的角度重新审视这些现象，发展了一种改进的幂级数方法，用于$(p,q)$-形式和复结构的变形。通过弗洛里切尔谱序列，我们证明在自然的偏消失条件下，所有障碍类都位于相应收缩映射的核中。这给出了一个改进的Kodaira原理，恢复并严格扩展了已知的结果。作为主要应用，我们获得了具有平凡canonical包的紧复流形的新无障碍准则。
英文摘要：
The Kodaira principle asserts that suitable cohomological contraction maps annihilate obstructions to deforming complex structures. In this paper, we revisit these phenomena from a purely analytic point of view, developing a refined power series method for the deformation of $(p,q)$-forms and complex structures. Working with the Frölicher spectral sequence, we show that under natural partial vanishing conditions on its differentials, all obstruction classes lie in the kernel of the corresponding contraction maps. This yields a refined Kodaira principle that recovers and strictly extends the known results. As a main application, we obtain new unobstructedness criteria for compact complex manifolds with trivial canonical bundle.
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