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Discriminants of convex curves are homeomorphic

Authors:	B Shapiro

Institution:	Department of Mathematics, University of Stockholm, S-10691, Sweden

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.

Keywords:	Convex curves discriminants

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