The Chord Construction
Abstract
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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.