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On two conjectures concerning convex curves
Moscow Oil and Gas Institute.
Stockholm University, Faculty of Science, Department of Mathematics.
2005 (English)In: International Journal of Mathematics, ISSN 0129-167X, Internat. J. Math., Vol. 16, no 10, 1157-1173 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we recall two basic conjectures on the developables of convex projective curves, prove one of them and disprove the other in the first nontrivial case of curves in RP3. Namely, we show that i) the tangent developable of any convex curve in RP3 has degree 4 and ii) construct an example of 4 tangent lines to a convex curve in RP3 such that no real line intersects all four of them. The question (discussed in [EG1] and [So4]) whether the second conjecture is true in the special case of rational normal curves still remains open.

Place, publisher, year, edition, pages
2005. Vol. 16, no 10, 1157-1173 p.
Keyword [en]
projective convexity; Schubert calculus
National Category
URN: urn:nbn:se:su:diva-20610OAI: diva2:187136
Available from: 2010-12-31 Created: 2007-11-28 Last updated: 2011-06-20Bibliographically approved

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