A transcendental approach to injectivity theorem for log canonical pairs
A transcendental approach to injectivity theorem for log canonical pairs
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DOI：
10.2422/2036-2145.201702_018
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发表时间：
2016-07
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通讯作者：
Shin-ichi Matsumura
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文献类型：
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作者：
Shin-ichi Matsumura
在本文中，我们研究对数正则对伴随丛的上同调群的超越方面，旨在建立对数正则奇点的解析理论。因此，在纯对数终端对的情况下，我们给出了霍奇理论最初证明的单射性定理的解析证明。我们的方法基于调和积分理论和 dbar 方程的 L2 方法，它使我们能够将单射性定理推广到复杂的解析设置。
In this paper, we study transcendental aspects of the cohomology groups of adjoint bundles of log canonical pairs, aiming to establish an analytic theory for log canonical singularities. As a result, in the case of purely log terminal pairs, we give an analytic proof of the injectivity theorem originally proved by the Hodge theory. Our method is based on the theory of harmonic integrals and the L2-method for the dbar-equation, and it enables us to generalize the injectivity theorem to the complex analytic setting.