The Chord Construction

Details The Chord Construction The Chord Construction

2001-10-31

arxiv.org/abs/math/0110338v1

Mathematics

Algebraic Geometry

5 pages, LaTeX 2e amsart

Scientific paper

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

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