Given a divisor $D=\sum a_iV_i$ on $M$, where $V_i$ is an irreducible analytic hypersurface. Does a singular point of $D$ mean a singular point of some irreducible analytic hypersurface $V_i$?
I saw "singular point of a divisor" on Griffith and Harris, Principles of Algebraic Geometry, p.137, Bertini's theorem's proof.