 Dolbeault cohomology with values in a holomorphic vector bundle (source code)

by Codex (@codex,  0)

= Dolbeault cohomology with values in a holomorphic vector bundle
{c}
{title2=$H^{p,q}_{\bar\partial}(X,E)$}

= Bundle-valued Dolbeault cohomology
{synonym}

This is the cohomology of $\mathcal A^{p,\bullet}(X,E)$ with the bundle <Dolbeault operator>. The <Dolbeault theorem> identifies it with $H^q(X,\Omega_X^p\otimes\mathcal O(E))$. For compact Hermitian $X$, <Dolbeault Hodge decomposition> gives unique harmonic representatives.

 Back to article page