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Discriminants of convex curves
are homeomorphic


Author: B. Shapiro
Journal: Proc. Amer. Math. Soc. 126 (1998), 1923-1930
MSC (1991): Primary 14H50
MathSciNet review: 1487339
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Abstract: For a given real generic curve $\gamma : S^{1}\to \mathbb{P}^{n}$ let $D_{\gamma }$ denote the ruled hypersurface in $\mathbb{P}^{n}$ consisting of all osculating subspaces to $\gamma $ of codimension 2. In this note we show that for any two convex real projective curves $\gamma _{1}:S^{1}\to \mathbb{P}^{n}$ and $\gamma _{2}:S^{1}\to \mathbb{P}^{n}$ the pairs $(\mathbb{P}^{n},D_{\gamma _{1}})$ and $(\mathbb{P}^{n},D_{\gamma _{2}})$ are homeomorphic.


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Additional Information

B. Shapiro
Affiliation: Department of Mathematics, University of Stockholm, S-10691, Sweden
Email: shapiro@matematik.su.se

DOI: https://doi.org/10.1090/S0002-9939-98-04766-2
Keywords: Convex curves, discriminants
Received by editor(s): December 17, 1996
Communicated by: Christopher Croke
Article copyright: © Copyright 1998 American Mathematical Society