2 problems

Let $X$ be a smooth complex $n$-dimensional algebraic variety, let $f\in\operatorname{\mathcal O}_X(X)$ be nonzero, and let $P\in X$ be a point in the zero-locus of $f$ such that…

Let $X$ be a smooth complex $n$-dimensional algebraic variety, let $f\in\operatorname{\mathcal O}_X(X)$ be nonzero, and let $P\in X$ be a point in the zero-locus of $f$ such that…