Geometry of Deligne cohomology
Geometry of Deligne cohomology
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德利涅上同调的几何
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
P. Gajer
中科院分区：
文献类型：
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作者：
P. Gajer
众所周知，二次Deligne上同调群可以等同于具有联络的全纯线丛的同构类的群。由于J-L的贡献，也有三次Deligne上同调的几何描述。Brylinski和P. Deligne，在连接结构和弯曲的gerbes方面。本文利用具有k-联络的高阶线丛的等价类，给出了任意次Deligne上同调的几何解释。本文还证明了经典的Abel-Jacobi同构$Pic^0（X）cong J（X）$推广到了具有$k$-联络的拓扑平凡1-全纯高阶线丛的等价类群与Griffiths中间Jacobian之间的同构.
It is well known that degree two Deligne cohomology groups can be identified with groups of isomorphism classes of holomorphic line bundles with connections. There is also a geometric description of degree three Deligne cohomology, due to J-L. Brylinski and P. Deligne, in terms of gerbes with connective structures and curvings. This paper gives a geometric interpretation of Deligne cohomology of all degrees, in terms of equivalence classes of higher line bundles with $k$-connections. It is also shown that the classical Abel-Jacobi isomorphism $Pic^0(X) cong J(X)$ generalizes to the isomorphism between groups of equivalence classes of topologically trivial 1-holomorphic higher line bundles with $k$-connections and Griffiths intermediate Jacobians.