= Tangent line to a projective plane curve
{title2=$T_pC$}
= Projective tangent line
{synonym}
For a <projective plane curve> $C=V(F)$ and a nonsingular <projective point> $p$, the tangent is the line $F_x(p)x+F_y(p)y+F_z(p)z=0$. The coefficients are not all zero, and the <Euler theorem for homogeneous functions> makes this line pass through $p$. On an affine chart this is precisely the first-order part of a local defining equation, so the definition agrees with the usual <tangent line> and is invariant under <projective transformations>.
Back to article page
