论文标题
双重违法行为和鸡巴二元性
Double transgressions and Bott-Chern duality
论文作者
论文摘要
我们提出了一个一般框架，用于在复杂的歧管上获得汇率双重侵犯公式，该公式可以看作是鸡巴校正二元性的表现。这些结果一方面补充了Harvey-Lawson获得的简单违法公式，另一方面，Bismut-Gillet-Soulé的双侵犯公式。 在应用程序中，我们提到了用于Bott-Chern的同谋的Gysin同构，这是一个抽象的Poincaré-Lelong-Lelang-Lelanger公式，用于Holomororphic和Hermitian和Hermitian Vector捆绑包，Andersson对标准Poincaré-lellong的概括，暗示了对Chern-Chern-Fullity fors of Chern-fulto for Singlos-Fullity for Singlos-Fullity forsergulton for Singbulton forsive for Singlielton forsival-fullto siply-fullto siply-ful quillen超级连接的Chern特征与自我婚姻，奇怪的内态性相关。 bismut-gillet-soulé双重侵犯的存在，没有沿亚曼福尔德的变性假设脱颖而出，并基于对形态添加操作的线性对应关系的扩展。最后，作为一个副产品，我们还获得了关于沿不可还原分量的复杂歧管的分析亚samuel多样性的{点定位}的陈述。
We present a general framework for obtaining currential double transgression formulas on complex manifolds which can be seen as manifestations of Bott-Chern Duality. These results complement on one hand the simple transgression formulas obtained by Harvey -Lawson and on the other hand the double transgression formulas of Bismut-Gillet-Soulé. Among the applications we mention a Gysin isomorphism for Bott-Chern cohomology, an abstract Poincaré-Lelong formula for sections of holomorphic and Hermitian vector bundles implying Andersson's generalization of the standard Poincaré-Lelong, a Bott-Chern duality formula for the Chern-Fulton classes of singular varieties or a refinement of the first author's simple transgression formula for the Chern character of a Quillen superconnection associated to a self-adjoint, odd endomorphism. The existence of a Bismut-Gillet-Soulé double transgression without the hypothesis of degeneration along a submanifold stands out and is based on an extension to linear correspondences of the operation of morphism addition. Finally, as a by-product we also obtain a statement about the {pointwise localization} of the Samuel multiplicity of an analytic subvariety of a complex manifold along an irreducible component.
