### Abstract

From an irreducible complete immersed curve X in a projective space ℙ other than a line, one obtains a curve X^{ ′} in a Graasmann manifold G of lines in ℙ that is the image of X under the Gauss map, which is defined by the embedded tangents of X. The main result of this article clarifies in case of positive characteristic what curves X have the same X′: It is shown that X is uniquely determined by X′ if X, or equivalently X′, has geometric genus at least two, and that for curves X_{ 1} and X_{ 2} with X_{ 1} ≠X_{ 2} in ℙ, if X′_{1} =X′_{2} in G and either X_{ 1} or X_{ 2} is reflexive, then both X_{ 1} and X_{ 2} are rational or supersingular elliptic; moreover, examples of smooth X_{ 1} and X_{ 2} in that case are given.

Original language | English |
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Pages (from-to) | 249-258 |

Number of pages | 10 |

Journal | Manuscripta Mathematica |

Volume | 80 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1993 Dec |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)