= Bertini smoothness theorem
{c}
{title2=$\operatorname{Sing}(D_{\mathrm{general}})\subseteq\operatorname{Bs}|D|$}
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.
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