D-bar Spark Theory and Deligne Cohomology

Details D-bar Spark Theory and Deligne Cohomology D-bar Spark Theory and Deligne Cohomology

2008-08-12

arxiv.org/abs/0808.1741v4

Mathematics

Algebraic Geometry

33 pages

Scientific paper

We study the Harvey-Lawson spark characters of level p on complex manifolds. Presenting Deligne cohomology classes by sparks of level $p$, we give an explicit analytic product formula for Deligne cohomology. We also define refined Chern classes in Deligne cohomology for holomorphic vector bundles over complex manifolds. Applications to algebraic cycles are given. A Bott-type vanishing theorem in Deligne cohomology for holomorphic foliations is established. A general construction of Nadel-type invariants is given together with a new proof of Nadel's conjecture.

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