Bertini smoothness theorem ($\mathrm{Sing}(D_{\mathrm{general}})\subseteq \mathrm{Bs}|D|$)

On a smooth variety over a field of characteristic zero, a general member of a basepoint-free linear system of divisors is smooth. More generally it is smooth outside the base locus. Irreducibility is a separate assertion and requires suitable hypotheses on the associated morphism; a pencil composed with a map to a curve can have disconnected general divisors.