On two conjectures concerning convex curves

Details On two conjectures concerning convex curves On two conjectures concerning convex curves

2002-08-28

arxiv.org/abs/math/0208218v2

Mathematics

Algebraic Geometry

AMSTEX, 15 pages, 3 eps pictures. to appear in Int. J. Math

Scientific paper

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.

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