Support dimension of a coherent sheaf
= Support dimension of a coherent sheaf
{title2=$\dim\operatorname{Supp}\mathcal F$}
The support dimension is the <dimension of a scheme> of the closed support of a <coherent sheaf>. Tensoring with a <line bundle> leaves its support unchanged. Quotienting by a section that avoids its <associated points> reduces the support dimension by at least one.