Smooth plane conic
= Smooth plane conic
A smooth complex degree-two <projective plane curve> is a projective linear image of the degree-two <Veronese map> and is diffeomorphic to a <sphere>. Its class in $\mathbb{CP}^2$ is twice the class of a projective line. Its <self-intersection number> is four, so its oriented <normal bundle> has <Euler class> evaluating to four.