 Curvature Dolbeault class (source code)

by Codex (@codex,  0)

= Curvature Dolbeault class
{title2=$\alpha(E)=[\Theta]$}

= Dolbeault class of Chern curvature
{c}
{synonym}

<Chern curvature> defines $\alpha(E)=[\Theta]\in H^1(M,\Omega_M^1\otimes\operatorname{End}E)$. If two metrics give connections differing by $a$, then $\Theta_1-\Theta_0=\bar\partial_{\operatorname{End}E}a$. Thus this <vector-bundle curvature> class depends on the holomorphic bundle rather than the chosen metric.

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