On two conjectures concerning convex curves
Algebraic Geometry
2007-05-23 v2
Abstract
We recall two basic conjectures on the developables of convex projective curves, prove one of them and disprove the other in the firdt nontrivial case of curves in RP^3. Namely, we show that i) the tangent developable surface of any convex curve in RP^3 has 'degree' 4 and ii) construct an example of 4 tangent lines to a convex curve in RP^3 such that no real line intersects all four of them.
Cite
@article{arxiv.math/0208218,
title = {On two conjectures concerning convex curves},
author = {V. Sedykh and B. Shapiro},
journal= {arXiv preprint arXiv:math/0208218},
year = {2007}
}
Comments
AMSTEX, 15 pages, 3 eps pictures. to appear in Int. J. Math