Associated point of a coherent sheaf
= Associated point of a coherent sheaf
= Associated point
{synonym}
An associated point of a <coherent sheaf> is a point whose corresponding prime is the annihilator of an element of the module on an affine chart. There are finitely many on a <Noetherian scheme>. A section of a <line bundle> avoiding them acts injectively on the sheaf, even when the scheme is nonreduced. Over an infinite field a sufficiently ample linear system supplies such a section.