Rational principal part
= Rational principal part
{title2=$\operatorname{Rat}(\mathcal F)/\mathcal F_P$}
For a <locally free sheaf> on an <irreducible variety>, the stalk inclusion identifies sections regular near $P$ inside its <rational sections>. The quotient records the obstruction to regularity at that point. This definition does not assume a nonsingular point or a discrete valuation parameter.