The Chord Construction

الأصل · EN

Let F be a smooth plane curve of degree 3. Let be an element in Pic(F)[2]-0. Let us define F':=p(p+)|p in F⊂(P²)*. In this note we show that F' is a smooth embedding of F/. Moreover, let ' be the generator of Pic(F)/, and let p in F be a flex, then p(p+)+' is a flex on F'. We present two proofs.