Reduced plane curve
= Reduced plane curve
A <projective plane curve> is reduced when its defining <homogeneous polynomial> is a <squarefree polynomial>, so no <irreducible component> is repeated. Its degree is the sum of the degrees of its distinct <irreducible components>. This convention is essential when bounding the number of <singular points>: the nonreduced equation $L^2=0$ has vanishing first <partial derivatives> at every point of its supporting line.