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Results tagged with hodge-theory
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user 16702
The study of harmonic differential forms on complex projective varieties, their invariantly defined filtrations, their integrals over topological cycles, especially over subvarieties, the deformations of these integrals and filtrations in families, and a multitude of generalizations.
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Formal adjoint of the covariant derivative
Ad 1: Yes, there is. The formula is
$$\nabla^*(X^\flat \otimes u) = - \nabla_X u -\mathrm{div}(X) \cdot u,$$
as can easily seen by local computation. Here, $X$ is a vector field and $X^\flat$ is the d …
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