紧Kähler流形的导数复形、BGG对应和数值不等式
Derivative complex, BGG correspondence, and numerical inequalities for compact Kähler manifolds
摘要：
紧Kähler流形的典范丛的上同调代数自然地被看作是外代数上的模。我们使用Bernstein-Gel'fand-Gel'fand对应，以及一般消失理论，以了解这个模块的正则性。我们还将它与准正则空间内的正则线性级数的无穷小理论联系起来。最后，我们在多项式环上应用向量丛方法，得到了不含非正则纤维化的紧致Kähler流形的全纯欧拉示性数和Hodge数的不等式。
英文摘要：
The cohomology algebra of the canonical bundle of a compact Kähler manifold is naturally viewed as a module over an exterior algebra. We use the Bernstein-Gel'fand-Gel'fand correspondence, together with Generic Vanishing theory, in order to understand the regularity properties of this module. We also relate it to the infinitesimal theory of the canonical linear series inside paracanonical space. Finally, we apply vector bundle methods on the polynomial ring side to obtain inequalities for the holomorphic Euler characteristic and the Hodge numbers of compact Kähler manifolds without irregular fibrations.
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