The Chord Construction
Algebraic Geometry
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0110338,
title = {The Chord Construction},
author = {D. Lehavi and R. Livné},
journal= {arXiv preprint arXiv:math/0110338},
year = {2007}
}
Comments
5 pages, LaTeX 2e amsart